Where to find the Kinsey Institute--and new insights into family structure and life history.

By Alfred Kinsey’s account, he had a strained relationship with his father. Kinsey’s father wanted his son to succeed in a profession like engineering, and to stand tall as a religious man. Though Kinsey’s father was certainly present, in early adulthood Kinsey would need to break away from that oppressive oversight to find a path of his own and one ultimately of great prominence. Alfred Kinsey would earn a PhD at Harvard in biology, and then accept a faculty position at Indiana University. He continued his studies of gall wasps, only later shifting his scholarly eye to that peculiar organism, the human being. Struck by his own (e.g., a virgin at the time of marriage) and his students’ poor grasp of sexuality, Kinsey would make this the focus of his future work. While Kinsey and his research team would conduct thousands of interviews and write two major works on human sexuality, the data garnered from those massive mid-twentieth century efforts would remain in an archive (what is now the Kinsey Institute), only seldom dug up and featured in a new study.

To investigate relationships between family structure and subsequent life history traits, Paula Sheppard, Justin Garcia and Rebecca Sear recently published a paper in PLoS ONE that drew upon this rich Kinsey dataset. The data stemmed from over 16,000 interviews with adults aged 18 and older, a slight majority of those with men. While interviews were conducted between 1938 and 1963, these recalled events happening earlier in most interviewees’ lives, making this a record of predominantly early 20th century family structure and life history in the U.S. The data were not drawn from a probability sample, leaving them vulnerable to sampling criticisms, as were raised at the time of the original research. Nonetheless, the data also bypass some of the prevailing constraints on more current data sets: these Kinsey data include both men and women, encompass a variety of family structures, embrace a wide array of life history variables covering puberty, sex, reproduction and risk-taking, and enable connecting early and later life history events from individuals’ lives.

Family structure was divided into eight categories, though the key findings of this study can be understood with respect to intact (mother and father present); father-absent (single mother or mother with stepfather); and mother-absent (single father or father with stepmother) households. Family structure referred to the time when a subject was between 6-8 years of age. The dependent variables were age at puberty, age at first petting, premarital sex, number of sexual partners, progression to first sex, extramarital sex, progression to first marriage, having more than one marriage, age at first birth, gambling, and use of illegal drugs. Key control variables were socioeconomic status (of parents at the time the subject was 14-17 years of age), number of siblings, age of puberty, ethnicity, year of birth and birth order.

What did these analyses reveal about links between family structure (during an individual’s mid-childhood) and subsequent pubertal, sexual, reproductive, and risk-taking profiles? Many of the dependent variables did not differ in relation to household structure. As an example, age of first petting was generally lower among individuals from mother and father-absent households, but with the exception of females raised by a mother and stepfather those differences were not significant. The majority of the life history variables differed depending on parental socioeconomic status (e.g., individuals whose parents were of higher socioeconomic status had later ages of first sex, marriage and first birth), demonstrating why it is important to control for socioeconomic status (as this study did) in investigating relationships between family structure and later life history. Consistent with more recent data from high-income, low-fertility contexts, this Kinsey-based study also found some delays in life history traits among individuals from intact households. Importantly, however, those differences were largely traced to accelerated life history variables among individuals from father-absent families rather than mother-absent families. As examples, individuals from father-absent households had earlier ages of first sex, more premarital sex, engaged in more gambling and had higher illegal drug use, with some of those patterns specific to males or females, although overall sex differences in those linkages were not prominent. The take-home message of the study could be that in a large, rich older American dataset there were many life history variables that did not differ by family structure, and for those that did differ by family structure they were more often associated with father absence.

As the authors discuss, those patterns are consistent with some models of family dynamics and life history that emphasize the role of fathers rather than some larger concept of risk per se. These findings also stand against the backdrop of some other studies situated in higher-fertility contexts in which father absence has been associated with delays in children’s life history progressions (rather than accelerations). As an example, Brooke Scelza found that father absence among the Martu of Australia was associated with a son’s later age of initiation. The present study thus adds to the mix of work investigating potential influences of fathers on children. In drawing upon the Kinsey archives, we see new ways in which fathers might shape the lives of the next generation. And for Kinsey himself, we might imagine how the intense presence of his father may have impacted not just the son, but the very study of human sexuality itself, eventually giving rise to the present analysis linking fathers and offspring life history.

Reference: Sheppard, P., Garcia, J.R., & Sear, R. (2014). A not-so-grim tale: How childhood family structure influences reproductive and risk-taking outcomes in a Historical U.S. population. PLoS ONE, 9, e89539.

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Journal of Neurophysiology

The influence of a 5-wk whole body vibration on electrophysiological properties of rat hindlimb spinal motoneurons

M. Bączyk, A. Hałuszka, W. Mrówczyński, J. Celichowski, P. Krutki

The study aimed at determining the influence of a whole body vibration (WBV) on electrophysiological properties of spinal motoneurons. The WBV training was performed on adult male Wistar rats, 5 days a week, for 5 wk, and each daily session consisted of four 30-s runs of vibration at 50 Hz. Motoneuron properties were investigated intracellularly during experiments on deeply anesthetized animals. The experimental group subjected to the WBV consisted of seven rats, and the control group of nine rats. The WBV treatment induced no significant changes in the passive membrane properties of motoneurons. However, the WBV-evoked adaptations in excitability and firing properties were observed, and they were limited to fast-type motoneurons. A significant decrease in rheobase current and a decrease in the minimum and the maximum currents required to evoke steady-state firing in motoneurons were revealed. These changes resulted in a leftward shift of the frequency-current relationship, combined with an increase in slope of this curve. The functional relevance of the described adaptive changes is the ability of fast motoneurons of rats subjected to the WBV to produce series of action potentials at higher frequencies in a response to the same intensity of activation. Previous studies proved that WBV induces changes in the contractile parameters predominantly of fast motor units (MUs). The data obtained in our experiment shed a new light to possible explanation of these results, suggesting that neuronal factors also play a substantial role in MU adaptation.

  • motoneuron
  • membrane properties
  • training
  • whole body vibration
  • rat

whole body vibration (WBV) is now widely applied as a form of physical training or as a rehabilitation method preventing muscle force decrease. It is generally accepted that WBV induces acute responses of the neuromuscular system, yet the actual effects on skeletal muscle contractile activity as well as mechanisms of influence on motoneurons and motor units (MUs) are vague. The most noticeable is an enhancement in muscle electromyographic (EMG) activity (Abercromby et al. 2007; Roelants et al. 2006), most likely elicited on a basis of the tonic vibration reflex (Romaiguère et al. 1993). There have been indirect observations that during the WBV exposition, high-threshold, fast fatigable MUs are more frequently activated (Pollock et al. 2012; Rittweger et al. 2000). The studies of Wakeling et al. (2002) and Wakeling and Liphardt (2006) support this thesis. The authors have reported high-frequency components within the spectral pattern of EMG recorded during pulsed and continuous WBV, which suggests that fast rather than slow MUs are actively involved in muscle tuning of the vertical oscillations. From the above reasons, the WBV training has been adapted to increase muscle strength and power as both acute (Cochrane et al. 2010; Cochrane and Stannard 2005; Cormie et al. 2006) and chronic (Bogaerts et al. 2007; Delecluse et al. 2003) treatment.

The recent studies on adaptations in MU contractile properties following a 5-wk WBV (Celichowski and Krutki 2012; Łochyński et al. 2009) have revealed that fast MUs are principally affected, and the changes are manifested by an increase in the maximum tetanic force of FF MUs, a shortening of a twitch contraction and a decrease in the twitch-to-tetanus ratio of FR units. Apart from intramuscular mechanisms responsible for these adaptations, changes in the electrophysiological properties of motoneurons should also be considered, as they influence the MU recruitment threshold and firing rates. However, so far there have been no studies investigating influence of the WBV on motoneurons.

It has been well documented in several reports that motoneurons are highly susceptible to altered levels of physical activity. Adaptations to an increased or a decreased functional motor demand can be observed as early as after 2–4 wk of an altered motor behavior (Cormery et al. 2000, 2005). Considerable changes in passive or active membrane properties, motoneuron excitability, or firing properties have been established in rat spinal motoneurons as effects of spontaneous running or a locomotor training (Beaumont and Gardiner 2002, 2003), in muscle unweighting (Cormery et al. 2005) or tetrodoxin-induced paralysis (Cormery et al. 2000).

The aim of our study was to determine whether a short-term (5-wk) WBV treatment has measurable effects on the electrophysiological properties of motoneurons. The method of intracellular recordings from hindlimb motoneurons was applied. We used the same experimental model (adult male Wistar rats) and the identical protocol of the WBV training on a vibratory platform as in the previous investigations on WBV effects on MU properties (Łochyński et al. 2009) to gain the possibility to compare results of both studies. Thus, these experiments tested the hypothesis that adaptations occur mainly in the fast-type motoneurons, and relate to the ability of MUs to generate higher force. Understanding the effects of the WBV on motoneuron properties will contribute to our knowledge on spinal mechanisms involved in effects of vibrations and may help substantiate WBV training protocols, which are widely used in sport and rehabilitation.

Animal housing.

The study was performed on 16 adult male Wistar rats (body mass 440–470 g), which were assigned to the experimental group of rats subjected to the WBV (n = 7), and the control group (C) (n = 9). Animals were housed in standard cages (2/each), in a room with humidity and temperature maintained constant, with the 12/12-h dark/light daily cycle, and had unrestricted access to food and water. All experimental procedures were approved by the Local Ethics Committee. The rats' maintenance and care followed the European Union guidelines and the Polish Law on the Protection of Animals.

The WBV training was performed on a vibration platform (Power Plate), producing sinusoidal vertical vibrations, 5 days a week for 5 wk. Rats were placed in a plastic container, attached to the platform by rigid belts, and were allowed to move freely inside the container during the procedures. WBV was superimposed onto the animal standard cage activity, provoking corrective postural reactions and body-supporting activities during which fast MUs were activated (Gorassini et al. 2000; Grimby 1984). The maximal vertical displacement of a platform was 2.5 mm, and the maximal acceleration of vibrations (measured by accelerometer ACL300, Biometrics) reached 4.79 g of the gravitational acceleration on earth. Four bouts of 30-s vibrations separated by 60-s rest intervals were applied in each daily session. Thirty-second exposures were used to minimize the possibility of high-threshold MU derecruitment, observed during prolonged muscle vibration (Bongiovanni et al. 1990). Four repetitions of the WBV were used to fit in principles of strength-training protocols, which recommend a small number of repetitions during a short period to provoke strength rather than endurance adaptations in a muscle (Ratamess et al. 2009). Vibration frequency was set to 50 Hz, since oscillations of hindlimb muscles during natural activity are estimated to be within a range between 30 and 50 Hz (Ettema and Huijing 1994).

All procedures were performed under pentobarbital anesthesia (initial dose 60 mg/kg ip). The depth of anesthesia was controlled by lack of withdrawal reflexes during preparation and the continuous ECG monitoring of the heart rate (300–360 bpm) during the recording session. Additional doses of anesthetics (10 mg/kg) were given when the heart rate rose, and experiments were not continued when the heart rate continuously decreased. Rats were artificially ventilated (Columbus Instruments; volume 4–5 ml, stroke rate 100–120/min), and expired CO2 level was measured (CAPSTAR-100, CWE) and maintained between 2 and 4% by adjusting tidal volume or ventilation rate. Pancuronium bromide (Pancuronium, Jelfa, Poland) was administered at regular intervals (the first dose of 0.4 mg/kg iv, supplementary doses of 0.2 mg/kg, applied every 30 min) to induce paralysis when recording from the motoneurons. At the end of each experiment, rats were euthanized by an overdose of pentobarbital (180 mg/kg). The femoral vein was catheterized for drug administration. Tracheotomy was made and a tracheal tube was inserted for artificial ventilation. The sciatic nerve (Sci) and its branches to the medial gastrocnemius (MG) and lateral gastrocnemius and soleus muscles (LGS) were dissected and placed on bipolar silver wire electrodes for stimulation. A laminectomy over L4–L5 segments was performed. Animals were fixed in a stereotaxic frame by clamps, the dura mater covering the spinal cord was incised, and small holes were made in the pia for insertion of glass micropipettes. Before the search for motoneurons, a pneumothorax was performed on the side of recordings by an incision between ribs (Th5–Th6). Small pools formed by skin over the exposed spinal cord and the sciatic nerve were filled with paraffin oil. The rat body temperature was kept within physiological limits (37 ± 1°C) by a thermostatically controlled heating system.

Stimulation and recording.

Glass micropipettes (tips broken to 1.5–2.0 μm in diameter, impedances of 5–15 MΩ) filled with 2 M potassium citrate solution were introduced into the gray matter of L4–L5 spinal cord segments, using a remotely controlled stepping micromanipulator (Källström, Sweden). Nerves were stimulated by electrical pulses (3 Hz, 0.1-ms duration, supramaximal amplitude up to 0.5 V) generated by a square pulse stimulator (GRASS Instruments, model S88). Antidromic action potentials from single motoneurons were recognized by a positive, all or nothing overshoot of the membrane potential and by a constant latency of an antidromic spike. All recordings were amplified (Axon Instruments, AxoClamp model 2B), passed via an analog-to-digital 10-bit converter at a sampling rate of 100 kHz, and stored on a PC for postexperimental analysis. Only stable recordings from motoneurons with the resting membrane potentials of at least −50 mV and the amplitudes of action potentials over 50 mV were taken into consideration (Gardiner 1993; Gardiner and Kernell 1990). After successful impalement of a motoneuron, antidromic action potentials were recorded in a bridge mode, and 10 spikes were averaged. From the obtained antidromic recordings, basic membrane properties were calculated: the resting membrane potential; the action potential amplitude; the action potential duration; the action potential rise time; the afterhyperpolarization amplitude; the AHP time-to-peak; and the AHP half-decay time (AHP-HDT). The latter parameter was used to separate fast from slow motoneurons: AHP-HDT was ≤20 ms for fast and >20 ms for slow motoneurons (Beaumont and Gardiner 2002, 2003; Gardiner 1993).

Measurement of cell input resistance was performed from an average of 40 short pulses (100 ms) of 1-nA hyperpolarizing current recorded in a DCC mode (4–8 kHz). Rheobase was determined as a minimum amplitude of a 50-ms square-wave current resulting in spikes 50% of the time. After measuring the basic properties, the steady-state firing (SSF) was evoked in a series of 500-ms square pulses of depolarizing current injections at amplitudes increasing or decreasing in steps of 0.1–5 nA in a DCC mode. Stimulations were separated by 5-s intervals. The minimum and maximum currents for the SSF were measured, and minimum and maximum SSF frequencies were calculated from the last three interspike intervals during the 500-ms square pulse (Fig. 1). For each motoneuron, the frequency-current (f-I) relationship was plotted, and the f-I slope was determined. Moreover, from the recordings with 500-ms current injections, the doublet threshold (DT) was determined as a minimum current to evoke the initial doublet of action potentials (with the first interspike interval <10 ms), and the relative ratio of DT to rheobase (DT/Rh) was calculated.

Fig. 1.

Examples of the rheobase (A, F) and steady-state firing (SSF) recordings (B–E, G–J) for one fast and one slow motoneuron, after the whole body vibration (WBV) training. Note considerable differences between these two motoneurons with respect to the rheobase thresholds (A vs. F) as well as current intensities necessary to evoke the minimum SSF (B vs. G) and the maximum SSF (E vs. J). The respective frequencies of the minimum and maximum SSF for a fast motoneuron (39.5 Hz and 78.4 Hz) and for a slow one (14.2 Hz and 18.4 Hz) were calculated from the last three interspike intervals in rhythmic discharges observed throughout the whole 500-ms period of current application. Values of intracellular current intensities are given above each record.

Statistical analysis.

For statistical comparison between WBV and control groups, Student's t-test was used for data with equal variance and normal distribution, whereas U-Mann Whitney test was used for data with unequal variance and unequal distribution. Significance levels were set at P < 0.01 or P < 0.05.

A total of 174 motoneurons with stable recordings were analyzed: 93 in the WBV group, and 81 in the control group. 53 cells were antidromically identified as MG, 37 as LGS, and 84 as Sci motoneurons. 69 motoneurons in the WBV group (23 MG, 11 LGS, 35 Sci) and 65 in the control group (20 MG, 16 LGS, 29 Sci) were classified as fast, whereas 24 motoneurons in the WBV group (7 MG, 4 LGS, 13 Sci) and 16 in the control group (3 MG, 6 LGS, 7 Sci) were classified as slow.

Five-hundred-millisecond current steps were applied in a subset of motoneurons (n = 106), so the SSF properties, doublet threshold, and f-I relationship could be determined in a proportion of the whole sample: from 48 and 33 fast motoneurons, as well as 16 and 9 slow motoneurons of the WBV and control groups, respectively.

Passive and threshold properties.

All the passive membrane properties of motoneurons remained unchanged after the 5-wk WBV treatment (Table 1). However, significantly lower mean values of the rheobase (P < 0.05) and the doublet threshold (P < 0.01) were observed in fast-type motoneurons of the WBV group compared with the untrained control (Table 1), indicating an increase in excitability of these cells. The relative threshold for doublet generation (measured as a ratio of current necessary to evoke doublet to the rheobase) exceeded 2 times rheobase, and there were no differences between motoneurons of the C and WBV groups. It should be mentioned here that doublets were observed frequently when intensity of current injection into motoneurons increased, but not in all the cases. In the WBV group, doublets could be determined in all 48 fast, and in 13 out of 16 slow-type motoneurons, while in the control group in 30 out of 33 fast, and 8 out of 9 slow-type cells.

View this table:
Table 1.

Passive and threshold properties of motoneurons

Rhythmic firing properties.

Rhythmic firing responses were measured in a subset of motoneurons (Table 2). Examples of the steady-state firing for two motoneurons (fast and slow) from the WBV group are given in Fig. 1. The minimum and maximum frequencies during SSF were not different between control and WBV groups, neither for fast nor slow-type motoneurons (Fig. 2A). However, the 5-wk WBV treatment resulted in a significant decrease in the minimum SSF current (P < 0.05) and in the maximum SSF current (P < 0.01) in fast motoneurons (Table 2, Fig. 2B). No significant changes with respect to these parameters were found in slow motoneurons.

View this table:
Table 2.

Rhythmic firing properties of motoneurons

Fig. 2.

A: distribution of the minimum and maximum frequencies of SSF for slow and fast motoneurons of the control and WBV groups. B: distribution of the minimum and maximum SSF current values for slow and fast motoneurons of the control and WBV groups. Note that frequently similar or identical values were measured in different motoneurons that resulted in overlapping of symbols in the charts. Horizontal lines indicate mean values, and asterisks point to significant differences between the control and WBV groups (*−0.01 ≤P < 0.05; **−P < 0.01, the Mann-Whitney Rank Sum Test).

The above changes in rhythmic firing properties of fast motoneurons influenced f-I relationships, reflecting minimum and maximum SSF frequencies, minimum and maximum current thresholds for SSF, and f-I slopes. Figure 3 presents examples of such f-I relationships, illustrating differences between fast- and slow-type motoneurons as well as a tendency of adaptive changes observed in fast-type motoneurons following the WBV training. The f-I relationships for the whole sample of motoneurons is summarized in Fig. 4. The f-I relationship for fast-type motoneurons of the WBV group was shifted leftwards compared with the control group, which was evidenced by significantly lower currents necessary for both minimum and maximum SSF (Table 2). Moreover, an increased slope (from 2.85 Hz/nA to 4.51 Hz/nA, P < 0.01) of the f-I relationship was determined in the group of fast-type motoneurons following the WBV (Table 2). Again, no differences in f-I relationship were found between C and WBV groups of slow motoneurons, with only a minor tendency to a leftward shift of the f-I relationship.

Fig. 3.

Examples of frequency-current relationships for fast (A, C) and slow (B, D) motoneurons of control and WBV groups. Considerable differences are visible between fast and slow motoneurons with respect to the minimum and maximum SSF frequencies (A and C vs. B and D). Moreover, a substantial difference in the slope between fast motoneurons of the control and WBV groups is presented (A vs. C; note different scale on abscissa), the latter closer to values observed for slow-type MNs. The regression lines were plotted according to f = y0+ax equations with individual values of y0 = 6.5, a = 4.6 for A; y0 = −1.2, a = 7.7 for B; y0 = −4.1, a = 6.1 for C; y0 = −1.3, a=9.1 for D.

Fig. 4.

Summary of the frequency-current relationships for the whole sample of fast and slow motoneurons of the control and WBV groups. Note the significant effect of the WBV treatment on fast motoneurons, reflected by a change in the slope of the f-I relationship combined with a significant leftward shift towards values observed for slow motoneurons (*−0.01 ≤ P < 0.05, **−P < 0.01).

Diverse effects of the WBV on fast and slow motoneurons.

The study indicates that a short-term, 5-wk WBV is capable to induce type-specific adaptations in electrophysiological properties of rat spinal motoneurons. Changes in excitability and firing characteristics concerned only fast motoneurons, whereas membrane properties of slow motoneurons remained unaltered. The diversity of WBV-evoked responses between two types of motoneurons might partly be justified by the training characteristics that favor fast motoneurons with respect to their relative daily time of activity. As mentioned earlier, MUs (and their corresponding motoneurons) are usually recruited in accordance to Henneman's size principle (Henneman et al. 1965); however, significantly lower recruitment thresholds of entire populations of MUs have been observed during the WBV (Romaiguère et al. 1993). Therefore, a majority of MUs are probably activated during the WBV, which may lead to more frequent activation of fast MUs (Rittweger 2010). An additional activity time (up to 2 min daily during WBV sessions) would have negligible influence on slow MUs, as their average daily time of contractile activity is ∼5.3–8.4 h in rat muscles (Hennig and Lømo 1985). In contrast, a daily activity time of two subtypes of rat fast MUs is 23–72 min for fast resistant and only 0.5–3 min for fast fatigable MUs, respectively (Hennig and Lømo 1985). Hence, the daily activity time can be increased during the 120-s WBV training maximally by 2.8–8.7% for fast resistant and even by 67–400% for fast fatigable MUs.

Another explanation of more frequent activation of fast motoneurons might be training kinematics, forcing the hindlimb muscles to act as spring-like elements to compensate the body dislocation induced by the vibration (Rittweger 2010). Analysis of the EMG spectral pattern has proven that mostly fast MUs (and fast motoneurons), capable to develop high levels of force in short time periods, are involved in the damping tasks (Wakeling et al. 2002; Wakeling and Liphardt 2006).

Moreover, a character of training might also benefit to activation of fast-type motoneurons, as during each WBV session on a vibratory platform the animals were forced to maintain balance on the moving bedding of the container (see materials and methods). Such balance maintenance requires strong activation of the cerebellum as well as the vestibulo- and rubrospinal tracts, which have stronger synaptic connections to fast than to slow motoneurons (Binder et al. 2002), which further favors their recruitment in stabilization tasks during the WBV (Gorassini et al. 2000).

Adaptations in threshold and rhythmic properties of motoneurons.

In this study, several threshold and rhythmic properties of fast-type motoneurons were altered by the WBV, without corresponding significant alterations of the passive membrane properties (Tables 1 and 2). This is somehow surprising, as the previous studies have indicated that alterations of the basic properties induce alterations in the threshold and rhythmic properties (Gardiner et al. 2006). An increase in the cell excitability (expressed principally by a reduction in the rheobase, the minimum current necessary to evoke SSF, and an increase in the slope of f-I relationship) is generally linked to an increase in a cell's input resistance and the AHP amplitude; however, this was not the case in our study (Tables 1 and 2). Therefore, other factors should be considered as responsible for the observed changes after 5 wk of the WBV.

One may speculate about a possible increase in activation of specific persistent inward currents (PICs), which are known to decrease rheobase of motoneurons (Lee and Heckman 2000). A decrease in rheobase current and an increase in the f-I slope reported after the spinal cord transection (Button et al. 2008) have also been connected with the increase in PIC currents. However, in our study we did not measure PIC activation, as the use of pentobarbital anesthesia abolishes PICs in motoneurons (Button et al. 2006; Hultborn 1999; Hultborn and Kiehn 1992). Therefore, we can only hypothesize about a role of PIC activation in the observed WBV-evoked changes in motoneuronal properties. For another explanation, one might consider mechanisms of presynaptic inhibition. It has been suggested that presynaptic inhibition of Ia afferents is highly dependent on the type of muscle activation, as motor tasks involving high motor control result in the increase of presynaptic inhibition, contrary to its inhibition by more automated tasks (Tahayori and Koceja 2012). In our study, muscle activation during the WBV was more reflexive than controlled, and it is supposed that levels of Ia presynaptic inhibition became considerably downregulated. However, it is difficult to assess how alterations in presynaptic inhibition could have affected discharge properties of motoneurons using current clamp technique. One may conclude that the factors responsible for the change in excitability of fast motoneurons in this study must await explanation.

Functional considerations.

Lower values of rheobase current and a leftward shift of the f-I relationship observed for fast motoneurons after the 5-wk WBV program (Fig. 4) indicate their ability to become recruited earlier (and possibly more frequently) and to achieve the same or even higher firing rates at lower stimulus intensities compared with the control group. Thus, one might draw a conclusion that in the trained group, a weaker synaptic input was needed for a motoneuron activation. However, this leftward shift of the relationship was not followed by a decrease in the minimum or maximum SSF frequencies. Therefore, the motoneurons of WBV-treated animals maintained their ability to generate high frequency of discharges, necessary to evoke high levels of force, while the “cellular effort” needed to induce such activations was significantly lower.

The increased slope of the f-I relationship (Fig. 4) indicates higher susceptibility of fast motoneurons after the WBV to an increased or decreased intensity of a stimulus (i.e., more or less effective synaptic drive under natural conditions). Therefore, our study suggests that the WBV treatment can influence control of the force output of fast MUs. The instantaneous force developed by a MU during a tetanic contraction depends both on the interpulse interval in a motoneuronal discharge pattern and on the initial force level (Krutki et al. 2008). Modifications of a motoneuronal firing rate by small changes in intensity of depolarization current (i.e., strength of synaptic input) appear to be more effective in fast motoneurons after the WBV compared with control.

Whole body vibration has already become an attractive alternative treatment for the strength training regime. Various studies have shown that WBV may be beneficial for inducing strength gains (Delecluse et al. 2003), osteoporosis prevention (Belavý et al. 2009), poststroke conditioning (Van Nes et al. 2004), or prevention of muscle atrophy (Verschueren et al. 2004). However, there is still much debate about mechanisms involved in the observed adaptive changes in the neuromuscular system (Cochrane 2010). This is the first study to demonstrate directly that merely four bouts of 30-s WBV daily, performed for 5 wk, induce changes in electrophysiological properties of the spinal motoneurons, and therefore, is the first study to provide direct evidence on motoneuronal plasticity following the WBV. Our observations performed in rats cannot be easily verified in human subjects. They may, however, contribute to our understanding of neuronal adaptations to the WBV and serve as a source of likely explanations of the WBV-evoked adaptations in the neuromuscular system.

This study was funded by Polish National Science Center (NCN) Grant No. 2011/01/N/NZ4/04901.

M.B. and P.K. conception and design of research; M.B., A.H., W.M., and P.K. performed experiments; M.B., A.H., and P.K. analyzed data; M.B., W.M., J.C., and P.K. interpreted results of experiments; M.B. prepared figures; M.B., J.C., and P.K. drafted manuscript; M.B., J.C., and P.K. edited and revised manuscript; M.B., J.C., and P.K. approved final version of manuscript.

This study constitutes part of the doctoral thesis submitted by Marcin Bączyk.

View Abstract


• multiple response optimization;
  • dual response surfaces (DRS);
  • covariate effect;
  • goal programming (GP);
  • stochastic modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

In the models used in the design and analysis of experiments, several input variables can affect the response, or output variables. If the input variables are known and are controllable factors, their levels can be set so as to optimize the functions of the observed responses. However, some of the input variables may be ‘nuisance’ variables which are not of interest and may not be controllable. Montgomery1 categorizes such variables into three classes:

  • Known and controllable variables whose effects are not of interest as a factor. The statistical technique of blocking can be used to eliminate the effects of these variables on the statistical analysis and thus on model building. Examples are systematic variations caused by shifts of workers or differences between manufacturing lines.

  • Known and uncontrollable variables are often called covariates. As the variables are suspected to be important, their values should be measured during the experiment. Inclusion of the individual effects of covariates and their interactions with other variables can help to improve the modeling of the outputs. The chemical properties of raw materials are an example.

  • Unknown and uncontrollable variables, where the relevance of the factor is unknown, and it may change levels during the experiment. Atmospheric humidity or age of feedstock are examples in this class. Randomization is the design technique used to avoid bias from such nuisance factors.

In the analysis of complex systems there are, almost invariably, several responses. Optimization of multiple quality characteristics (or response variables) is more complicated than optimization of a single one since we face different units, importance, and optimality directions. In this study a multicovariate-multiresponse model has been developed in which the covariates have stochastic patterns and the aim is to find the best arrangement of the input variables including covariates and factors so as to optimize the response variables. This paper is organized as follows. In Sections 2.1 and 2.2, a literature review is presented for both covariate-oriented studies and stochastic multiresponse optimization (MRO). In Section 3, a general model for multicovariate-MRO is proposed and in Section 4, computational descriptions and other properties of the model are illustrated by two numerical examples. Finally, conclusions and key remarks are presented in Section 5.

2. Literature review

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

In this section some previous work on covariate analysis and multiple responses optimization are reviewed separately.

2.1. Earlier studies on covariate analysis

Most of the research in the field of covariate analysis is directed to the elimination of covariate effects on response variability so as to provide more reliable and accurate estimates of factor effects. A few studies have focused on optimization of the experiment in which responses are affected by covariates. The Analysis of Covariance (ANCOVA) is the primary method for adjusting the observed response variable for the effect of the covariate or concomitant variable. If such an adjustment is not performed, the covariate will inflate the error mean square and make it harder to detect true differences in the response due to treatments. Thus, the ANCOVA is a method of adjusting for the effects of an uncontrollable nuisance variable1. Three major limitations of ANCOVA are:

  • Response is linearly related to covariate. Thus, the interaction between covariates and factors or probable curvature in covariate effect may be disregarded.

  • Covariate values are not different among the groups and covariates are fixed.

  • If more than one covariate is considered, there is no collinearity between covariates.

Rahbar and Gardiner2 proposed a non-iterative method of estimation when the response is linearly related to the covariate. Their method was nonparametric, with a single, integer-valued covariate. Gertsbakh3 considered life testing with factorial experiments and tried to find the best allocation of testing position and time. The response variable was assumed to have an exponential distribution and the parameters were estimated by maximum likelihood. This research includes multiple covariates and factors. Wu4 studied covariate effects in nonlinear mixed-effect models and used maximum likelihood to estimate the regression coefficients. In addition, a computationally efficient method for approximate likelihood inference was proposed to overcome computational difficulties such as the non-convergence caused by the nonlinear functions and high dimensional integrals of complete-data log-likelihood. Royston and Sauerbrei5 proposed a new approach for analyzing covariates with preliminary linear transformation of covariates producing less extreme leverage. Their method is related to fractional polynomial modeling and the proposed transformation incorporated a predefined shift of the origin away from zero. They confirm the reliability and stability of univariate or multivariable fractional polynomial models. Yeo6 proposed a new form of generalized additive model including the distribution function of the mean response and a weighted linear combination of distribution functions of covariates. This form avoids structural problems in linking the mean response and covariates. Markov-chain Monte-Carlo methods were used to estimate the parameters within a Bayesian framework. Das et al.7 considered RBD, BIBD, and CRD designs in which covariates were analyzed. They proposed are optimal structure for each of the aforesaid designs for better and more reliable analysis of covariates.

2.2. Multiresponse optimization

Different aspects of MRO problems have been studied in several areas. We can distinguish three general categories: (a) Desirability functions: in this category, researchers try to aggregate information from each response to obtain one response. Optimization is then performed on a single total desirability function. (b) Priority-based methods: If the responses have differing degrees of importance degrees, we first consider the most important response for optimization. If the solution is not unique, then find the best solution by comparing the status of the other responses for alternative solutions. These steps are repeated until all responses have been considered and a unique optimal solution found. (c) Loss function: In this category, based on the Taguchi loss function, all response values are aggregated and converted into one. Much research has been dedicated to developing and generalizing the Taguchi loss function for many specific cases.

The earlier work in MRO includes Layne8 who presented a procedure that simultaneously considers three functions—the weighted loss function, the desirability function, and a distance function—to determine the optimum parameter combination. Pignatiello9 utilized a variance component and the squared deviation-from-target to form an expected loss function to optimize a multiple response problem. However, this method is difficult to implement. The first reason is that a cost matrix must be initially obtained, and the second reason is that it needs much experimental data. Leon10 presented a method, which is based on the notion of a standardized loss function with specification limits. However, only the nominally-the best (NTB) characteristic is suitable for this approach, which may limit the capability of the method. Ames et al.11 presented a quality loss function approach in the response surface. The basic strategy is to describe the response surfaces with experimentally derived polynomials, which can be combined into a single loss function using known or desired targets; minimizing the loss function with respect to process inputs, locates the best operating conditions. Bashiri and Hejazi12 used Multiple Attribute Decision Making (MADM) methods, such as VIKOR, PROMETHEE II, ELECTRE III, and TOPSIS, to convert multiresponses to a single response in order to analyze robust experimental designs. The main advantage of their method was the consideration of standard deviation that was included in the robust experimental design. Also, because only one response regression function was fitted, the proposed method decreased statistical error. Tong et al.13 used the VIKOR method in converting Taguchi criteria to a single response and then found a regression model and the related optimal setting. Tong et al.14 also considered correlation of responses and used PCA and TOPSIS methods to find the best variable setting. Chiao and Hamada15 considered experiments with correlated multiple responses whose means, variances, and correlations depend on experimental factors. Analysis of these experiments consists of modeling distributional parameters in terms of the experimental factors and finding factor settings that maximize the probability of being in a specification region, i.e. all responses are simultaneously meeting their respective specifications. Kazemzadeh et al.16 proposed a general framework for MRO problems based on goal programming (GP), studied some existing works, and attempted to aggregate all the characteristics into one approach. Shah et al.17 illustrated the seemingly unrelated regression (SUR) method for estimating the regression parameters that may be useful when the response variables are correlated. Their method can lead to more precise estimation of the optimum variable setting. Bashiri et al.18, from the viewpoint of multiple objective decision making, proposed an approach in which Global Criteria (GC) have been applied to aggregate multiresponse surfaces in the simulation of a probabilistic inventory model. Kovach and Cho19 used a robust design and proposed MRO using nonlinear GP. They also used a combined array for incorporating the nuisance factors. Table I gives a summary of this literature together with comparisons of the existing methods and of the proposed procedure.

Table I. Some earlier works and their comparison
MethodsNo. of covariatesCorrelationInteraction effectsStochastic covariateResponse linearityFocus on statistical aspectsFocus on optimization aspectsRobustness
Rahbar andSingle
Gertsbakh3Multiple Between factors
Das et al.7Multiple
Wu4MultipleBetween covariatesBetween factors
Kazemzadeh Between responsesBetween factors
et al.16
Chiao and  Between factors
Shah et al.17 Between responsesBetween factors
ProposedMultipleBetweenFor all of the variables
method covariates(factors and covariates)

According to Table I, in the majority of publications on the effect of covariates, it is assumed that the relation between the response variables and covariates is linear and also that there is no interaction between factors and covariates. On the contrary, in this paper there is no limitation to the existence of interaction effects between any variables. Moreover, we try to maximize the occurrence probability of stochastic covariates.

3. Proposed approach

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

We develop an optimization model for multiresponse surfaces with probabilistic covariates in which response variation and covariate probability are considered as separate objective functions. In addition, the proposed approach makes it possible to solve the optimization with correlated or uncorrelated covariates. For this purpose, Principal Component Analysis (PCA) is used to get independent values from the original data. Figure 1 provides a general framework for the proposed approach.

thumbnail image

Figure 1. The proposed approach in schematic view

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Some advantages of the proposed approach are listed below to compare with other studies mentioned in the literature review.

  • In this paper, a systematic approach is proposed to optimize multiresponse surfaces with respect to factors and covariates for complex processes.

  • This approach has some capabilities to analyze multiresponse problems with consideration of probabilistic covariates.

  • There is no limitation to the distribution type of covariate probability.

  • There is no limitation to the definition region of covariates (i.e. integer, binary, positive, etc.).

  • The proposed approach can consider correlation between the covariates.

3.1. Multiresponse-multicovariate model

In this section, a multiobjective mathematical model is developed based on the experimental design to optimize the following three sets of objective functions:

  • Location effects: The expected values of the response surfaces are optimized according to the type of response variables (NTB, STB, and LTB responses).

  • Dispersion effects: The estimated variances of the response variables are minimized to ensure robustness in the results.

  • Probability functions of the covariates: Maximization of this objective set increases the reliability of the results. As the covariates are stochastic and uncontrollable, this objective ensures that the covariates will occur with maximum probability.

The constraints of the proposed model are related to specification limits of factors and the definition region of stochastic covariates. According to the aforementioned objectives and constraints the proposed mathematical model (a second-order polynomial) and related parameters are defined below:

Parameters and variables:

  • R: Response variables.

  • β, α, γ, β', α', γ': Regression coefficients.

  • x: Controllable variables.

  • c: Covariates.

  • f(Ci): Probability distribution function of the ith covariate.

  • (L, U): Lower and upper bound of controllable variables.

  • Ω: Feasible region of covariates (according to their probabilistic pattern).

Mathematical model:
  • equation image(1)
  • equation image(2)
  • equation image(3)
  • equation image(4)
  • equation image(5)

The first objective set (1) shows the response surfaces to be optimized by settings of the factors and covariates. The second objective set (2) ensures that the dispersion effects are considered and minimized and objective set (3) maximizes the covariates at their modes. Constraint sets (4) and (5) include the limits of the factors and define the region of the covariates. Depending on the number of covariates, there are two sub-procedures for analyzing the covariate effect:

  • Single covariate approach: In this case, a proper function between the real values of input variables (factors and covariates) and output variables (response surfaces for location and dispersion effects), is developed.

  • Multiple covariate approach: In this case, depending on the following criteria, two solution methods are proposed as follows:

    • Case 1: If the correlation between covariates is not statistically meaningful, the proper regression functions between input and output variables can be fitted directly. In this case, the joint mode of the covariates could be used in place of the third objective function set.

    • Case 2: If the covariates are highly correlated, the regression procedure will face a collinearity problem that makes regression analysis difficult. In this paper we use PCA to provide proper information from correlated data. Figure 2 shows the PCA phase (a part of Figure 1) in flowchart view.

thumbnail image

Figure 2. The PCA phase in flowchart view

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As shown in Figures 1 and 2, the proposed approach can be summarized in the following steps. The computational details are presented in the numerical examples.

  • Step 1: Identification of the factors, covariates, and responses. In addition, the continuous or discrete probability distributions for the covariates must be specified.

  • Step 2: Depending on the number of factors and the region determined by their limits, an appropriate design is selected for running the experiment.

  • Step 3: Depending on the number of covariates and their interdependencies, the proposed approach should be continued according to the following cases:

    • 3.1 If there is only one covariate, the general model can be applied and f(C) in (3) is defined as follows:

      • equation image(6)

      Note that, a is an adjusting parameter that makes it possible to find an interval for calculating the probability value of continuous random variables.

    • 3.2 If there are two or more covariates in the experiments, the general model must be modified according to the following conditions:

      • (a) In this case, the covariates are independent and one modification should be made in the general model in which fT(C) can be defined by the following relations:

        • equation image(7)

        • equation image

        where f(C) is obtained from (6) for continuous or discrete distribution functions.

      • (b) In this case there is interdependence between the covariates. In such situations the regression analysis might be affected by collinearity20. In this paper PCA is applied to overcome this problem by using linear transformations to convert a vector of correlated variables into those that are uncorrelated. Hotelling21 initially developed PCA to explain the variance–covariance structure of a set of variables by linearly combining the original variables. The PCA technique can account for most of the variations of the original p variables via k uncorrelated principal components, where kp. More formally, if C = c1, c2, …, cp is a set of original variables with a variance–covariance matrix and the set of uncorrelated linear combinations can be obtained as the matrix

        • equation image(8)

        where C′ = (c1, c2, …, cp)T, c1 is the first principal component, c2 is the second principal component and so on; A = (aij)P × P and A is an orthogonal matrix with ATA = I. Therefore, C can also be expressed as

        • equation image(9)

        where Aj = [a1j, a2j, …, apj]T is the jth eigenvector of equation image. After performing PCA on correlated covariates, fT(C) will change to:

        • equation image(10)

        • equation image

        Note that C′ is an uncorrelated vector with a linear relationship to C. In some cases, finding the distribution function for C′ is complicated; thus the second formulation of fT(C) in (10) could be used. More details of this step are illustrated in the numerical example.

  • Step 4: In this step, proper regression functions (response surfaces) are fitted between response variables and inputs (factors and covariates).

  • Step 5: Finally, in this step, after constructing the mathematical model, the optimal values of the responses and the related values for factors and covariates are found using the GP approach.

3.2. GP model

As mentioned in Step 5, the aforesaid three objective sets have been aggregated by GP method. In this section the goal function and the related constraints are presented.

Goal function:Min Z = [fµk(dµk, dµk), fσk(dσk, dσk), fpl(dpl, dpl)]

Subject to

For location effects:

  • equation image

where d and d′ are negative and positive deviations from the target and should be minimized in the goal function.

For dispersion effects: equation image

As the variance cannot be negative, in this relation the target of response variance is set to zero and only positive deviation is allowed and should be minimized in the goal function.

For covariate probability: Probability function(cl) − dpl = Tll = 1, 2, …, m

Tl is a positive target for the occurrence probability of each covariate. Note that this target is a lower bound or minimum acceptable value for the probability, hence the positive deviation from the target should be maximized in the goal function.

For controllable factors: lixiuii = 1, 2, …, n

The upper and lower bounds for each factor is determined in the experimental design depending on the specification limits.

For covariates: cl∈Θ

where Θ is the definition region of the covariates according to the probabilistic distributions or stochastic patterns which are known.

For deviation variables: dk, dk, dl≥0∀k = 1, 2, …, p;∀l = 1, 2, …, m

In the proposed model, summation of the normalized weighted deviations is used to aggregate the objective function so that the final GP model can be expressed as:

  • equation image

Subject to

  • equation image

where W is a vector of importance degrees obtained from decision makers and equation image nd equation image are the standard deviation of the mean and variance of kth response variables, respectively, in experimental observations. Thus W/σ and W/T are the vectors of normalized weights used in the final additive objective so as to make it weighted and dimensionless.

In Section 3 we have described the proposed approach and the related mathematical model and given details of the steps. In the following section this approach will be illustrated through two numerical examples and the benefits and efficiencies assessed. Also some comparative results between the proposed method and some existing methods are presented.

4. Numerical examples

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

In this section, two cases are studied to illustrate the applications of the proposed approach. In the first experiment there are two factors and one normally distributed covariate that might affect two responses. The data are generated from three replicates of a Central Composite Design (CCD). Table II shows more information about these experiments.

Table II. Experimental data for case 1
   Response variables
FactorsCovariatesExpected valueEstimated variance
ABXN(15, 42)equation imageequation imageequation imageequation image
  Desired value366.2500
  Standard deviation5.222.6641.09170.477

As presented in Table II, the two responses (µ1, µ2) represent the location effects of the input variables, whereas the other responses equation image represent the dispersion effects used in dual response modeling. The fitted response surfaces for a simulated data set, obtained using the MINITAB software package, can be written as:

  • equation image

where X is single covariate and it is known that XN(15, 42). The response variables are of type NTB with desired values equation image. According to the response surfaces and desired values of each response, the mathematical model of the optimization problem can be formulated as

  • equation image

Subject to

  • equation image

In this example, the desired probability value of the covariate occurrence is initially set to 0.19 and, later, sensitivity analysis for this parameter and its effects on the results will be performed (this is an adjustable parameter that might be obtained by interaction between the analyst and decision maker). This parameter is a lower bound for the occurrence probability of covariates; greater values of this parameter make the feasible region tighter and the results more reliable. In this example all objective function sets have equal weights, that is wi = 1. Table III shows the optimum results for Case 1 obtained using the LINGO 8 optimization software.

Table III. Optimum solution for case 1 and comparison
Optimum valuesABXequation imageequation imageequation imageequation imagef(c ± α)
Proposed method−0.2414−0.71413.8812366.251.860.6890.19
Kim and Lin230.47660.2912.0533.365.7221.330.790.15
Kovach and Cho190.0153−0.079212.767366.251.50.9250.169

Considering the experimental data in Table II and the optimum values in Table III, it is clear that the proposed method has satisfied all response function constraints, including two location effects (µ1, µ2), two dispersion effects equation image, and one covariate expectation. Table IV shows the results of MANCOVA for the fitted response surfaces and also includes some measures for comparison. MANCOVA and its optimization phase have been performed in MINITAB 15 statistical software.

Table IV. Optimum solution for case 1 using MANCOVA in Minitab 15
Optimum valuesABXequation imageequation imageequation imageequation imagef(c ± α)
MANCOVA (Minitab)10.10622.156331.53616.85352.85571.41090.041
Proposed method-0.2414-0.71413.8812366.251.860.6890.19

For sensitivity analysis of the optimization model, contour plots of the response surfaces as functions of the input variable are shown in Figure 3.

thumbnail image

Figure 3. Contour plots of response surfaces for case 1

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In Figure 3, we have set the third variable at its optimum value. In the right section of Figure 3, B is set to −0.714 and in the left section, A is set to 0.2414. It is clear in Figure 3, that if the covariate increases above its optimum value, the feasible region of the model becomes tighter. But small changes in the values of the controllable variables do not lead to unacceptable response values. As mentioned above the proposed method not only maximized the expected value of the covariate, but also satisfied all of the constraints on the response variables including location and dispersion effects.

Previously the target value of covariate probability was set to 0.19. Increasing this value makes the problem infeasible and in order to perform sensitivity analysis on this parameter it has been varied in the reasonable range. Figure 4 shows the effect of this parameter on location and dispersion effects and Figure 4 shows the sensitivity of goal function and covariate probability with respect to this parameter compared to each other.

thumbnail image

Figure 4. Sensitivity analysis of covariate probability and goal function

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Figure 4 shows that in this example, increasing the desired value of covariate probability has an inverse relationship with goodness of optimal goal function which should be minimized. In addition, greater values of this parameter could lead to a more reliable result since the optimum covariate value may occur with higher probability. But in this example, if this parameter takes a value greater than 0.19, the model will be infeasible. The effect of changing this parameter on each response variable can be found in Figure 5. This figure shows that this parameter has different effects on equation image and equation image, while two location effects are not sensitive with respect to this parameter.

thumbnail image

Figure 5. Sensitivity analysis of location and dispersion effects

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We now consider Case 2, a multicovariate model. As shown in Table V, the second case has two response variables (R1 and R2), three factors (A, B, and C) and two covariates (C1 and C2). The response variables are of type NTB and their desired values are equation image. In addition, the covariates have the probability distributions

  • equation image

In this case we ran a single replication of the design. As a result, dispersion effects cannot be considered.

Table V. Experimental data for case 2

The correlation between C1 and C2 is 0.865. Owing to the resulting collinearity between the predictor variables, we use PCA to provide a linear transformation to uncorrelated variables. Table VI shows the analysis using MINITAB 15 statistical software.

Table VI. Principal component analysis for two correlated covariates

According to Table VI, the required transformation of the two covariates to make them uncorrelated is:

  • equation image(11)
  • equation image(12)

By inverting (11) and (12) the original values of covariates can be obtained from (13) and (14):

  • equation image(13)
  • equation image(14)

Using PCA the regression function between inputs and outputs can be fitted more reliably. The two fitted response surfaces are

  • equation image

In this case all response sets have equal weights of importance (wi = 1). Now the final GP model can be written as follows.

  • equation image

Subject to

  • equation image(15)
  • equation image(16)
  • equation image(17)
  • equation image(18)
  • equation image(19)
  • equation image(20)

Similar to the first example, the objective of this model is to minimize the summation of standardized weighted deviations of targets. Constraints set (15) calculates the deviation from the target of NTB response variables. The next set is to find the optimum covariates that satisfy the minimum acceptable probability for occurrence which equals 0.05 for both exponential and Poisson covariates. The effect of changing this parameter on the results was elaborated previously in the first example. The linear relation between PCs and covariates are entered in the model by relations (17). The next three constraint sets (sets 20–23) show the limits of the decision variables depending on their definitions.

Table VII gives the optimal values of each variable resulting from optimization of the proposed model. This problem has also been solved using Minitab software24. The Minitab software provides MRO module in which the desirability function method is used to analyze such problems.

Table VII. Optimization results—case 2
Optimal valuesABCPC1PC2C1C2R1R2f(C1)f(C2 ± α)
Proposed methods-0.536-0.671.6555.4187.1990.2405.50.1250.077
Desirability function1.51-1.6818-0.181719.66405.50.0130.0015

As shown in Table VII, R1 and R2 reach their goals and the probability functions of the covariates have proper values. Although the desirability function method has also satisfied two response variables (R1, R2), it is obvious that the probability value of covariates occurrence resulted by the proposed method is considerably better than the desirability method. In other words, if we set factors as (A, B, C) = (1.51, −1.68, −0.18), we cannot expect that the responses will be satisfied unless the covariates are observed as (C1, C2) = (17, 19.66). Therefore, since these values of covariates occur with smaller probability, the factor setting will not be sufficiently reliable.

5. Conclusion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

In this paper, a mathematical model has been developed to find the best settings of variables to optimize dual response models when single or multiple stochastic covariates are included in the experiments. In the case of collinearity among the covariates, the capability of the proposed approach has been improved by the use of PCA. As the optimum values of the covariates must be analyzed from a probabilistic viewpoint, optimizing the response variables by ignoring the covariates would be misleading. A second important point is that the proposed model tries to find the best factor levels considering the maximum probable values of each covariate according to their stochastic patterns, that is their probability distributions. Two numerical examples have been analyzed and the main conditions and calculation steps of the proposed approach are described in detail.

Biographical Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information

Authors' biographies

Taha Hossein Hejazi received an MSc in Industrial Engineering from Shahed University, Tehran. His primary research interests include quality control and engineering, optimization and design of experiments, computer simulation, metaheuristics for optimization and Multiple Criteria Decision Making. Also he will start PhD programs at Amirkabir University of Technology (Tehran Polytechnic) in the next semester and he is a member of the International Association of Computer Science and Information Technology (IACSIT).

Mahdi Bashiri is an Assistant Professor at Shahed University. He received his BS in Industrial Engineering from Iran University of science and technology in 1999 and his MS and PhD in Industrial Engineering from the Tarbiat Modares University of Tehran in 2001 and 2005, respectively. He visited the statistics department at London School of Economics and political sciences at 2004 for six months. His research interests are Multiple Response Optimization, Design of Experiments and Facility Location and Layout.

Kazem Noghondarian is an Assistant Professor of Industrial Engineering at Iran University of Science and Technology. He received his BSc from University of Neveda and his MSc and PhD from Arizona State University and University of British Columbia (UBC), respectively. His primary research interests include statistical quality control, quality management, design of experiments, data mining and simulation.

Anthony C. Atkinson is Emeritus Professor of Statistics at the London School of Economics and Political Science. He received his MA in Chemical Engineering from Cambridge University in 1960 and his MSc and PhD in Statistics from Imperial College, London in 1965 and 1970. His primary research interests include: clinical trials; generalized linear models; simulation; robust statistical methods; regression diagnostics and optimum experimental design. He was editor of the Journal of the Royal Statistical Society, Series B and an associate editor of Biometrika and Technometrics. Professor Atkinson is a Fellow of the American Statistical Association.

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Literature review
  5. 3. Proposed approach
  6. 4. Numerical examples
  7. 5. Conclusion
  8. Biographical Information
  • 1
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    Rahbar MH, Gardiner JC. Nonparametric estimation of regression parameters from censored data with a discrete covariate. Journal of Statistical and Probability Letters 1995; 24:1320.
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    Gertsbakh J. Optimal allocation of test position and testing time in a factorial life testing experiment. Journal of Statistical and Probability Letters 1996; 26:249258.
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    Wu L. A computationally efficient method for nonlinear mixed-effects models with nonignorable missing data in time-varying covariates. Computational Statistics and Data Analysis 2007; 5:24102419.
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Question by  siva (28)

Should I euthanize my dog?

Answer by  Dontbugme (697)

This would depend on your reason for doing so. If the dog is very old and sick, deaf, blind, or has no quality of life, I think euthanizing would be the right thing to do. If you just don't want the dog anymore, take it to the Humane Society.

Answer by  Anna27 (62)

Choosing to put a pet to sleep is not a task to be taken lightly. If your dog is suffering, euthanasia is an option that you should talk about with your vet.

Answer by  Gabriel (2146)

Is it terminally ill? Has the vet recommended that you put it down? Is there a chance for recovery? If your dog is really ill, with no chance to recover, the merciful thing may be to euthanize it. Otherwise, see if there is a no-kill shelter in your area.

Answer by  bsatterfield (131)

If the dog is suffering and in pain. My dog of twelve years had a stroke in which it couldn't control its back legs or bowl movements. I decided that was an appropriate reason to euthanize her. If the dog is just annoying then no.

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Military Funeral Customs

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This custom began during the Napoleonic Wars (1706-1815). The dead carried from the field of battle on a caisson were covered with a flag. When the U.S. flag covers the casket, it is placed so the union blue field is at the head and over the left shoulder. It is not placed in the grave and is not allowed to touch the ground.

Flags are provided for burial services of service members and veterans. The flag for one who dies on active duty is provided by one's branch of service. Flags for other veterans are provided by the Department of Veterans Affairs. The flag is presented to the next of kin at the end of the funeral, usually by the military chaplain. If there is no next of kin present, the flag may be presented to the veteran's close friend or associate if requested. The flags that have draped the caskets of the Unknown Soldiers are on display in the Memorial Display Room of the Memorial Amphitheater.

The custom of firing cannon salutes originated in the British Navy. When a cannon was fired, it partially disarmed the ship. Therefore, firing a cannon in salute symbolizes respect and trust. THESE SALUTES ARE FIRED ONE AFTER ANOTHER.

This practice originated in the old custom of halting the fighting to remove the dead from the battlefield. Once each army had cleared its dead, it would fire three volleys to indicate that the dead had been cared for and that they were ready to go back to the fight. CONTRARY TO PUBLIC OPINION, The fact that the firing party sometimes consists of seven riflemen, FIRING 3 VOLLEYS OVER THE CASKET DOES NOT SIGNIFY A 21 GUN SALUTE.

All personal salutes may be traced to the prevailing use in earlier days to ensure that the saluter placed himself in an unarmed position. Salute by gunfire is a most-ancient ceremony. The British for years compelled weaker nations to make the first salute, but in time international practice compelled "Gun for Gun" in the principle of an equality of nations.

In the earliest days, seven guns was a recognized British National Salute. Those early regulations stated that, although a ship could fire only seven guns, the forts could fire for honors three shots to one shot afloat. In that day powder of sodium nitrate was easier to keep on shore than at sea. In time, when the quality of gun powder improved by the use of potassium nitrate, the sea salute was made equal to the shore salute -- 21 guns as the highest national honor. Although for a period of time, monarchies received more guns than republics, eventually republics claimed equality.

There was much confusion caused by the varying customs of maritime states, but finally the British government proposed to the United States a regulation that provided for "Salute to be Returned Gun for Gun." The British at that time officially considered the international salute to be 21 guns and the United States adopted the 21-gun and "Gun for Gun Return" August 17, 1875. Previous to that time, our national salute was one gun for each state. The practice was also a result of usage -- John Paul Jones saluted France with 13 guns (one for each state) at Quiberon Bay when the Stars and Stripes received its first salute. This practice was not authorized until 1810.

By the admission of states to the Union, the salute reached 21 guns by 1818. In 1841, the national salute was reduced to 21 guns. In fact, the 1875 adoption of the British suggestion because a formal announcement that the United States recognized 21 guns as an international salute. THESE SALUTES ARE FIRED ONE AFTER ANOTHER AND THE NUMBER OF GUNS IS BASED ON THE RANK OF THE PERSON BEING SALUTED. The President of the United States and other heads of State rate 21 guns.


Making the Most of LinkedIn
It has become increasingly important to develop “networking savvy” for success in a job or internship search. Networking is still the number one way people find jobs. Since this is the case, we want to provide you with some pointers, some caveats and some general guidelines on how you might use the professional networking site LinkedIn to be more effective in your networking efforts.
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FAQs for students participating in Mentoring.
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Total Time
Prep 7 mins
Cook 3 mins

I eat green smoothies most days as my breakfast/lunch. I vary them according to what we have, but this has been my recent base recipe.

Ingredients Nutrition

  1. Place ingredients in the order listed in a vitamix blender.
  2. Blend until smooth.
  3. You can use other blenders, but your smoothie will not come out as smooth.


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Tutorial: The Technology of MIDI

Part 1: Overview

MIDI Cables & Connectors
MIDI Messages
Standard MIDI Files

MIDI (pronounced "mid-e") is a technology that makes creating, playing, or just learning about music easier and more rewarding.

Playing a musical instrument can provide a lifetime of enjoyment and friendship. Whether your goal is to play in a band, or you just want to perform privately in your home, or you want to develop your skills as a music composer or arranger, MIDI can help.

How Does MIDI Work?

There are many different kinds of devices that use MIDI, from cell phones to music keyboards to personal computers. The one thing all MIDI devices have in common is that they speak the "language" of MIDI. This language describes the process of playing music in much the same manner as sheet music: there are MIDI Messages that describe what notes are to be played and for how long, as well as the tempo, which instruments are to be played, and at what relative volumes.

Because MIDI data is only performance instructions and not a digital version of a sound recording, it is actually possible to change the performance, whether that means changing just one note played incorrectly, or changing all of them to perform the song in an entirely new key or at a different tempo, or on different instruments.

MIDI data can be transmitted electronically between MIDI-compatible musical instruments, or stored in a Standard MIDI File for later playback. In either case, the resulting performance will depend on how the receiving device interprets the performance instructions, just as it would in the case of a human performer reading sheet music. The ability to fix, change, add, remove, speed up or slow down any part of a musical performance is exactly why MIDI is so valuable for creating, playing and learning about music.

Three Kinds of MIDI

The original Musical Instrument Digital Interface (MIDI) specification defined a physical connector and message format for connecting devices and controlling them in "real time". A few years later Standard MIDI Files were developed as a storage format so performance information could be recalled at a later date. The three parts of MIDI are often just referred to as "MIDI ", even though they are distinctly different parts with different characteristics.

The MIDI Messages specification (or "MIDI Protocol") is probably the most important part of MIDI. Though originally intended just for use with the MIDI DIN transport (see Part 2) as a means to connect two keyboards, MIDI messages are now used inside computers and cell phones to generate music, and transported over any number of professional and consumer interfaces (USB, FireWire, etc.) to a wide variety of MIDI-equipped devices. There are different message groups for different applications, only some of which are we able to explain here. (Part 2)

There are also many different Cables & Connectors that are used to transport MIDI data between devices. The "MIDI DIN" transport causes a lot of confusion because it  has specific characteristics which some people associate as characteristics of "MIDI" -- forgetting that the MIDI-DIN characteristics go away when using MIDI over other transports (and inside a computer). With computers a High Speed Serial, USB or FireWire connection is more common. Each transport has its own performance characteristics which might make some difference in specific applications, but in general the transport is the least important part of MIDI, as long as it allows you to connect all the devices you want use! (Part 3)

The final part of MIDI are the Standard MIDI Files (and variants), which are used to distribute music playable on MIDI players of both the hardware and software variety. All popular computer platforms can play MIDI files (*.mid) and there are thousands of web sites offering files for sale or even for free. Anyone can make a MIDI file using commercial (or free) software that is readily available, and many people do, with a wide variety of results. Whether or not you like a specific MIDI file can depend on how well it was created, and how accurately your synthesizer plays the file... not all synthesizers are the same, and unless yours is similar to that of the file composer, what you hear may not be at all what he or she intended. (Part 4)

Even More MIDI

Over the past 20 years MMA member companies have created many extensions and enhancements to MIDI that are designed to address some of the issues mentioned briefly above. General MIDI (GM) and Downloadable Sounds (DLS) help address the issue of predictable playback from MIDI Files. Scalable Polyphony MIDI helped bring MIDI to mobile phones by providing a standard means for scaling playback of complex MIDI files across a variety of low-power handsets. More information on extensions and enhancements are available throughout this web site, especially in the TechSpecs area.

Many people today see MIDI as a way to accomplish something, rather than as a protocol, cable, or file format. For example, many musicians will say they "use MIDI", "compose in MIDI" or "create MIDI parts", which means they are sequencing MIDI events for playback via a synthesizer, rather than recording the audio that the synthesizer creates.

Use is prohibited without written permission.


Top Cars Deals in Waterville

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Waterville Rental Cars

Waterville is well known for its musicals, forests, culture, festivals, and hiking. Waterville is also popular for its dining, restaurants, university, shopping, and coffee.

Enjoy window shopping and do some people-watching in a few of the local stores and markets such as Turnpike Mall. Enjoy the atmosphere and browse through the shops at these colorful attractions. Keen nature lovers will be glad to find out that Waterville also has some ecological parks where families can enjoy picturesque scenery and some notable trees, plants and birds. To tour one of the local nature reserves, visit Capitol Park, Viles Arboretum, Kennebec River Rail Trail, or Augusta Mill Park. To catch live performances by some of the best and brightest talents in Waterville, see what's on at much-loved performance venues. For a memorable night out, take that someone special to the Waterville Opera House, which run a unique blend of shows.

Whether you’re road tripping through the state or venturing around the city, do yourself a favor and rent a car in Waterville, Maine. When you sit behind the wheel of your rental car, you can forget about hailing taxis and memorizing public transportation schedules. Because with access to a car rental in Waterville, you’re free to travel where and when you want. Thanks to a set of wheels, experience the freedom of exploring the entire area on your own watch. Spend the morning browsing a museum on one side of town and then hit up an attraction on the opposite side of town in the afternoon without a care in the world.

Explore Waterville

Explore Waterville with Expedia’s Travel Guides to find the best hotels, flights, vacation packages and more!


women's basketball

Several areas in Eugene were without power for about two hours Saturday afternoon. The outages started just before three p.m., affecting several thousand Eugene Water and Electric Board customers and a University of Oregon basketball game.

Four substations malfunctioned, taking out power to the U of O campus, and Whiteaker and Coburg Road neighborhoods. Traffic signals went dark during the outage and the second half of the women’s basketball game was delayed by over an hour while waiting for the power to come back on.

Jes Burns

Elaine Thompson - AP


Cusco, Peru on a Budget (Takes a Little Work)

Peru gets a lot of travelers, from budget backpackers to “money is no object” luxury travelers ticking off a box on their bucket list. Because of Machu Picchu being named one of the wonders of the world and Peru seemingly unable to stop milking that cash cow in all their marketing, an

The Toughest Two Hours in Peru

I’ve done a lot of hiking in Peru. I’ve gone on the Inca Trail, done the Salkantay Trek, and just finished up a version of the Lares Trek. But the hike that made me the most uneasy is one that up to 400 people a day set off to do: heading to

Don’t Hurry Through Peru

Sure, the famous citadel on a mountain is worth seeing sometime in your life and Cusco is a great city that still feels special despite the hordes of tourists. To really get how great Peru is though, you have to take some time to explore and soak it all in. A couple

Travel Bites from Mexico and Peru

I don’t do as much freelance writing as I used to since I’m busy enough running my online media company’s own blogs and websites, so I’ve gotten kind of slack about putting up links to travel stories I’ve written for other publications. Catch-up time now for ones from Peru and Mexico. A

Is Peru a Cheap Place to Travel? It Depends…

Peru is a travel bargain. Or Peru is very expensive. It all depends on how you travel. I inhabit the strange world of travel writing where for my job I go back and forth from cheap hotels to plush palaces, from crowded buses to executive taxis depending on the assignment. That shows


Total Time
Prep 10 mins
Cook 35 mins

I just threw this together one afternoon with things that I had lying around the house, and it turned out quite delicious! In case you've never encountered it, Braggs liquid aminos is a savory liquid made from soybeans that adds an interesting (very tasty) flavor. If you can't find Braggs, try using regular soy sauce or tamari instead. The brands of the ingredients really don't matter much, but I've parenthesized the brands I used for clarity.

Ingredients Nutrition

  1. Preheat oven to 375°F.
  2. Lightly sautee veggie ground round in olive oil. Once heated, add the vegetable broth, peas, and corn and cook on medium heat for 5-7 minutes. Add 2 T nutritional yeast, Braggs, and remaining spices.
  3. Pour vegetable mixture into ovenproof casserole dish (any size will work, but preferably smaller and deeper rather than larger and shallower). Layer mashed potatoes on top of vegetable mixture.
  4. Melt 2 T vegan margarine. Add 2 T nutritional yeast and mix well. Pour this mixture over the mashed potatoes.
  5. Cook pie uncovered for about 35 minutes.


Suri Cruise, 16 months, cozies into mom Katie Holmes' arms for a nap during a whirlwind Parisian day trip Thursday that brought them to the Louvre for a private tour and then along the Rue St. Honoré for shopping.


Recreational Salmon Fishing
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How to Catch Salmon

Marine Areas (Drifting/Trolling) Drift Fishing | Trolling

Two fishermen netting a salmonThis article describes the basics of saltwater salmon fishing from a boat for the beginning angler. It is intended only as a starting point, and is not meant to cover every aspect of salmon fishing. After getting your feet wet, a good angler will constantly search for additional information to improve their abilities and skills.

Knowing the habits of salmon is important for figuring out how to catch them. In general, each of the species can be found in the following areas:

Adult chinook salmon are usually found in two general habitats. Early in the morning or late in the evening, chinook can often be found cruising very close to shore, especially near kelp beds. At this time, they can be caught in 20’ to 120’ feet of water. They are most likely suspended in the water column, that is, they aren’t on the bottom. In open water, chinook are going to be found were there is abundant bait. They can be anywhere from in the top 20’ of water to down on the bottom at depths of 200’ or deeper. Usually they will move deeper during the day as the sun gets brighter. A good starting depth for open water is between 40’ and 80’.

These juvenile chinook are generally found within 10’ of the bottom at depths between 60’ and 150’. Occasionally they will be suspended, especially if there is lots of bait that is suspended.

Coho are an open water fish. The easiest way to find coho is to locate tide and/or current rips. These rips concentrate zooplankton and other invertebrates, which concentrate baitfish. Coho are often in the top 20’ of water, regardless of the time of day or weather. They can be found down to 70’ or 80’, but seldom are caught below 100’.

Pink are also an open water fish. However, they are not necessarily associated with tide rips. They can often be found at depths of 40’ to 80’.

Trolling consists of fishing out of a constantly moving boat. Trollers will use weights, divers, or downriggers to achieve a desired depth to present their bait or lures. Trolling is more effective than drift fishing when salmon are spread out over a large area. Trolling with a downrigger is probably the most popular method of salmon fishing in saltwater in Washington.\

Marine Areas 5, 6, and 7 Sockeye Fishing Techniques


by Douglas Hardwick

What Is Therapeutic Touch?

What Is Therapeutic Touch?
by Douglas Hardwick

Energy medicine is an approach to healing based on the assumption that there is a natural field of energy that surrounds and penetrates every living thing. Within such an approach, practitioners attempt to manipulate the field of energy to encourage healing. Most forms of energy medicine developed originally in Asia. Therapeutic Touch, however, developed within the American nursing tradition in the 1970's.

Therapeutic Touch assumes that an individual's body, mind, and spirit form a complex energy field that extends beyond the surface of the body. According to proponents of Therapeutic Touch, an individual's level of health reflects the flow of life energy in and through that individual. In a healthy person there is a symmetrical and balanced flow of energy within the individual and in exchange with the environment. The free flow of energy in this way nourishes the individual and promotes vitality. When illness occurs or an injury happens, the flow of energy becomes obstructed or constricted. It is the practitioner's task is to find the obstruction, clear it, and re-establish an unrestricted flow of energy.

People who seek intervention through Therapeutic Touch remain fully clothed and may sit up or lie down during a healing session. A Therapeutic Touch session follows a series of prescribed steps. First the practitioner centers self. This is a brief period of meditation and concentration during which the practitioner withdraws his or her attention from the external world. Here the practitioner develops the calm detachment and intent to heal required to participate in the healing process.

Next, the practitioner conducts an assessment of the person who has sought healing. In this phase, the practitioner places his or her hands, palms down, a few inches above the patient's body. The practitioner then moves his or her hands above the patient's body, in a rhythmical motion, from head to foot. The practitioner intuitively searches for the areas of constriction and imbalance in the patient's energy field. Practitioners are said to sense these areas through subtle, but distinct, sensations in their hands (heat, cold, tingling sensations, etc.).

Once an area of congestion is found, the third phase begins. This is the intervention phase during which the practitioner attempts to relieve the congestion and balance the energy field. To do so, the practitioner moves his of her hands in long sweeping motions starting above the point of congestion and moving toward the toes. This process, called "unruffling" is intended to smooth out the energy field and move stagnant energy away from the patient. The practitioner continues in this way until the unusual sensations associated with the congestion are no longer felt.

Next, the practitioner directs additional energy to the patient. By directing additional life energy to the patient, the practitioner is helping to make up for an energy deficit that develops during an illness. The additional energy is said to help the patient's own healing processes function more effectively.

Finally, the practitioner engages in a period of evaluation and closure. Here the practitioner reassesses the patient's energy field to determine whether constrictions were missed. The practitioner also solicits feedback from the patient. Together, these sources of information, along with the practitioner's own intuitions, determine the end of a session.

Therapeutic Touch is most often practiced by nurses, but practitioners may be found among physicians, physical therapists, naturopaths, chiropractors, and massage therapists. Practitioners of Therapeutic Touch see it as an important complement to conventional medical care. According to its proponents, Therapeutic Touch reduces pain and lowers anxiety. It is said to heal fractures and wounds and to clear infections faster than conventional approaches alone. It also may be useful in the treatment of certain allergies and addictions. The relaxation response that occurs during a Therapeutic Touch session is especially important. Deep relaxation reduces stress and lowers blood pressure. These effects alone are likely to promote greater levels of health and vitality. If you are interested in finding a qualified practitioner of Therapeutic Touch, you should contact the Nurse Healers-Professional Associates International.

About the Author

Douglas Hardwick, Ph.D., holds a doctorate in psychology from the University of Virginia. Dr. Hardwick has extensive interests in aging and holistic health issues. He developed the website: - a holistic health information hub


Iannis Xenakis 1922 - 2001

Xenakis is a leading avant-garde composer of the post-war era. He was educated in Greece, and became active in the resistance against Nazi occupation, which led to his imprisonment, violent injuries and his ultimately flight to France in 1947 to escape the death sentence. Having settled in Paris, he attended Messiaen's classes in 1952, and responded to the encouragement to develop an individual style based on his scientific training - indeed, he then very much followed his own path, avoiding existing styles, and the highly original music that resulted had its roots in architectural structures, mathematical processes and game theory.

Xenakis's orchestral works Metastaseis and Pithoprakta set him at the forefront of the avant-garde in late 1950s. He further explored complex rhythms and textures in ensemble works (such as Eonta and Akrata), and the culmination of that period came with the large-scale dramatic scores Oresteia and Kraanerg. He has composed prolifically, mainly for instrumental and orchestral forces, and his music is characterised by virtuosity, microtonal inflections, primal energy and ritualistic power.

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King Of Fighters Wing

Description: Fight against the computer as you setup your game, choose your character and try to win. . King Of Fighters Wing is a Fighting Games.

Instructions: Player 1:W, A, S, D keys -To move.
J - To enter.

Player 2: Arrow Keys - To move.
Numbers 1-6 - To attack.
Number 1 - To enter..

Fighting Games