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The Heun-Askey-Wilson algebra is introduced through generators $\{\boX,\boW\}$ and relations. These relations can be understood as an extension of the usual Askey-Wilson ones. A central element is given, and a canonical form of the Heun-Askey-Wilson algebra is presented. A homomorphism from the Heun-Askey-Wilson algebra to the Askey-Wilson one is identified. On the vector space of the polynomials in the variable $x=z+z^{-1}$, the Heun operator of Askey-Wilson type realizing $\boW$ can be characterized as the most general second order $q$-difference operator in the variable $z$ that maps polynomials of degree $n$ in $x=z+z^{-1}$ into polynomials of degree $n+1$., 16 pages

We consider the eigenvalue problem associated with the Dunkl-type differential operator (in which the reflection operator R is involved) L = dx R + v(x), (v(-x) = -v(x)), in the context of supersymmetric quantum mechanical models. By solving this eigenvalue prob- lem with the help of known exactly solvable potentials, we construct several classes of func- tions satisfying certain orthogonality relations. We call them the Dunkl-supersymmetric (Dunkl- SUSY) orthogonal functions. These functions can be expressed in terms of the classical orthog- onal polynomials (COPs). The key feature of these functions is that they appear by pairs, i.e., Qn(x) and Qn(−x) are both the eigenfunctions of L. A general formulation of the Dunkl-SUSY orthogonal polynomials is also presented.

We have previously shown how the Frontal Pole cortex (FPC) neurons play a unique role in both the monitoring and evaluating of self-generated decisions during feedback in a visually cued strategy task. For each trial of this task, a cue instructed one of two strategies: to either stay with the previous goal or shift to the alternative goal. Each cue was followed by a delay period, then each choice was followed by a feedback. FPC neurons show goal-selective activity exclusively during the feedback period. Here, we studied how neural correlation dynamically changes, along with a trial in FPC. We classified the cells as goal-selective and not goal-selective (NS) and analyzed the time-course of the cross-correlations in 76 pairs of neurons from each group. We compared a control epoch with the feedback epoch and we found higher correlations in the latter one between goal-selective neurons than between NS neurons, in which the correlated activity dropped during feedback. This supports the involvement of goal-selective cells in the evaluation of self-generated decisions at the feedback time. We also observed a dynamic change of the correlations in time, indicating that the connections among cell-assemblies were transient, changing between internal states at the feedback time. These results indicate that the changing of the pattern of neural correlations can underlie the flexibility of the prefrontal computations.

We give the automata which describe time evolution rules of the box-ball system (BBS) with a carrier. It can be shown by use of tropical geometry, such systems are ultradiscrete analogues of KdV equation. We discuss their relation with the lamplighter group generated by an automaton. We present spectral analysis of the stochastic matrices induced by these automata, and verify their spectral coincidence.

Diastolic wall strain (DWS) was reported as a simple and feasible echocardiographic index in assessing left ventricular (LV) diastolic stiffness. We sought to evaluate whether DWS predicts age-related cardiovascular events. Patients referred for transthoracic echocardiogram, those with preserved LV ejection fraction and no clinical heart failure were studied. Cardiovascular events were ascertained using Framingham criteria (myocardial infarction, coronary insufficiency, stroke, transient ischemic attack, congestive heart failure, or cardiovascular death). DWS was calculated with a validated formula. Cox proportional hazards modeling was used to assess the risk of cardiovascular events. Of a total number of 962 patients (mean age 60.9 ± 14.9 years, 48.0% men), 69 (7.2%) developed at least 1 cardiovascular event during a mean follow-up of 43 ± 32 months. After adjusting for cardiovascular comorbidities in a multivariable model, low DWS (≦ 0.33) was a significant independent predictor of cardiovascular events [hazard ratio (HR): 1.87, 95% confidential interval (CI) 1.04–3.36, P = 0.04]. Echocardiographic assessment of DWS may help in identifying the patients at increased risk for future age-related cardiovascular events.

Animals need to learn and to adapt to new and changing environments so that appropriate actions that lead to desirable outcomes are acquired within each context. The prefrontal cortex (PF) is known to underlie such function that directly implies that the outcome of each response must be represented in the brain for behavioral policies update. However, whether such PF signal is context dependent or it is a general representation beyond the specificity of a context is still unclear. Here, we analyzed the activity of neurons in the dorsolateral PF (PFdl) recorded while two monkeys performed two perceptual magnitude discrimination tasks. Both tasks were well known by the monkeys and unexpected changes did not occur but the difficulty of the task varied from trial to trial and thus the monkeys made mistakes in a proportion of trials. We show a context-independent coding of the response outcome with neurons maintaining similar selectivity in both task contexts. Using a classification method of the neural activity, we also show that the trial outcome could be well predicted from the activity of the same neurons in the two contexts. Altogether, our results provide evidence of high degree of outcome generality in PFdl.

Kuniba, Okado, Takagi and Yamada have found that the time-evolution of the Takahashi-Satsuma box-ball system can be linearized by considering rigged configurations associated with states of the box-ball system. We introduce a simple way to understand the rigged configuration of $\mathfrak{sl}_2$-type, and give an elementary proof of the linearization property. Our approach can be applied to a box-ball system with finite carrier, which is related to a discrete modified KdV equation, and also to the combinatorial $R$-matrix of $A_1^{(1)}$-type. We also discuss combinatorial statistics and related fermionic formulas associated with the states of the box-ball systems. A fermionic-type formula we obtain for the finite carrier case seems to be new.

An 82-year-old woman with symptomatic severe aortic stenosis was scheduled to undergo transcatheter aortic valve replacement (TAVR) under local anesthesia. Measurable calcifications were observed on the aortic valve ([Figure 1A][1]). Calculated aortic annulus area, perimeter, and minimum diameter

Patient initials or identifier number Y. N ### Relevant clinical history and physical exam We report a case of a 72-year-old woman who presented with left leg rest pain and small heel ulceration, a Rutherford classification of grade 5. She had past histories of old myocardial infarction

It is shown that the hopping of a single excitation on certain triangular spin lattices with non-uniform couplings and local magnetic fields can be described as the projections of quantum walks on graphs of the ordered Hamming scheme of depth 2. For some values of the parameters the models exhibit perfect state transfer between two summits of the lattice. Fractional revival is also observed in some instances. The bivariate Krawtchouk polynomials of the Tratnik type that form the eigenvalue matrices of the ordered Hamming scheme of depth 2 give the overlaps between the energy eigenstates and the occupational basis vectors., Comment: 12 pages, 4 figures, Submission to SciPost

We construct a non-trivial type of 1-step exceptional Bannai-Ito polynomials which satisfy discrete orthogonality by using a generalized Darboux transformation. In this generalization, the Darboux transformed Bannai-Ito operator is directly obtained through an intertwining relation. Moreover, the seed solution, which consists of a gauge factor and a polynomial part, plays an important role in the construction of these 1-step exceptional Bannai-Ito polynomials. And we show that there are 8 classes of gauge factors. We also provide the eigenfunctions of the corresponding multiple-step exceptional Bannai-Ito operator which can be expressed as a 3 x 3 determinant., Comment: 30 pages

An infinite-dimensional representation of the double affine Hecke algebra of rank 1 and type $$(C_1^{\vee },C_1)$$ in which all generators are tridiagonal is presented. This representation naturally leads to two systems of polynomials that are orthogonal on the unit circle. These polynomials can be considered as circle analogs of the Askey–Wilson polynomials. The corresponding polynomials orthogonal on an interval are constructed and discussed.

Schur-Delsarte-Genin (SDG) maps and Bannai-Ito polynomials are studied. SDG maps are related to dressing chains determined by qua- dratic algebras. The Bannai-Ito polynomials and their kernel polynomials - the complementary Bannai-Ito polynomials - are shown to arise in the frame- work of the SDG maps.

A construction is given of the most general representations of the q-oscillator algebra where both generators are tridiagonal. It is shown to be connected to the Askey-Wilson polynomials.

In this paper, a generalized E-transformation arising from the study of a generalization of sequence transformations and triangular recursion schemes is proposed. Three new algorithms, namely, the generalized E-algorithm, the generalized FS-algorithm and the generalized hungry type E-algorithm, are constructed for implementing the generalization of the E-transformation. Some convergence results of the generalized E-algorithm are obtained. In addition, some particular cases of the generalized E-transformation and the recursive algorithms for their computation are also studied.

This study aimed at investigating the effect of distraction on working memory and its underlying neural mechanisms in children with attention-deficit/hyperactivity disorder (ADHD). To this end, we studied hemodynamic activity in the prefrontal cortex using near-infrared spectroscopy while 16 children with ADHD and 10 typically developing (TD) children performed a working memory task. This task had two conditions: one involved a distraction during the memory delay interval, whereas the other had no systematic distraction. The ADHD patients showed significantly poorer behavioral performance compared with the TD group, particularly under the distraction. The ADHD group exhibited significantly higher level of prefrontal activation than did TD children. The activity level was positively correlated with the severity of ADHD symptoms. These results suggest that the impairment in the inhibition of distraction is responsible for the working memory deficits observed in ADHD children. Inefficient processing in the prefrontal cortex appears to underlie such deficits.

In previous reports, we described neuronal activity in the polar (PFp), dorsolateral (PFdl), and orbital (PFo) PFC as monkeys performed a cued strategy task with two spatial goals. On each trial, a cue instructed one of two strategies: Stay with the previous goal or shift to the alternative. A delay period followed each cue, and feedback followed each choice, also at a delay. Our initial analysis showed that the mean firing rate of a population of PFp cells encoded the goal chosen on a trial, but only near the time of feedback, not earlier in the trial. In contrast, PFdl cells encoded goals and strategies during the cue and delay periods, and PFo cells encoded strategies in those task periods. Both areas also signaled goals near feedback time. Here we analyzed trial-to-trial variability of neuronal firing, as measured by the Fano factor (FF): the ratio of variance to the mean. Goal-selective PFp neurons had two properties: (1) a lower FF from the beginning of the trial compared with PFp cells that did not encode goals and (2) a weak but significant inverse correlation between FF throughout a trial and the degree of goal selectivity at feedback time. Cells in PFdl and PFo showed neither of these properties. Our findings indicate that goal-selective PFp neurons were engaged in the task throughout a trial, although they only encoded goals near feedback time. Their lower FF could improve the ability of other cortical areas to decode its selected-goal signal.

The prefrontal cortex (PF) is involved in outcome-based flexible adaptation in a dynamically changing environment. The outcome signal dissipates gradually over time, but the temporal dynamics of this dissipation remains unknown. To examine this issue, we analyzed the outcome-related activity of PF neurons in 2 monkeys in a distance discrimination task. The initial prestimulus period of this task varied in duration, allowing us to dissociate the effects of time and event on the decline in previous outcome-related activity —previous correct versus previous error. We observed 2 types of decline in previous outcome representation: PF neurons that ceased to encode the previous outcome as time passed (time-dependent) and neurons that maintained their signal but it decreased rapidly after the occurrence of a new external event (event-dependent). Although the time-dependent dynamics explained the decline in a greater proportion of neurons, the event-dependent decline was also observed in a significant population of neurons.

Persymmetric Jacobi matrices are invariant under reflection with respect to the anti-diagonal. The associated orthogonal polynomials have distinctive properties that are discussed. They are found in particular to be also orthogonal on the restrictions either to the odd or to the even points of the complete orthogonality lattice. This is exploited to design very efficient inverse problem algorithms for the reconstruction of persymmetric Jacobi matrices from spectral points. Isospectral deformations of such matrices are also considered. Expressions for the associated polynomials and their weights are obtained in terms of the undeformed entities.

The estimation of space and time can interfere with each other, and neuroimaging studies have shown overlapping activation in the parietal and prefrontal cortical areas. We used duration and distance discrimination tasks to determine whether space and time share resources in prefrontal cortex (PF) neurons. Monkeys were required to report which of two stimuli, a red circle or blue square, presented sequentially, were longer and farther, respectively, in the duration and distance tasks. In a previous study, we showed that relative duration and distance are coded by different populations of neurons and that the only common representation is related to goal coding. Here, we examined the coding of absolute duration and distance. Our results support a model of independent coding of absolute duration and distance metrics by demonstrating that not only relative magnitude but also absolute magnitude are independently coded in the PF. NEW & NOTEWORTHY Human behavioral studies have shown that spatial and duration judgments can interfere with each other. We investigated the neural representation of such magnitudes in the prefrontal cortex. We found that the two magnitudes are independently coded by prefrontal neurons. We suggest that the interference among magnitude judgments might depend on the goal rather than the perceptual resource sharing.

The activity of some prefrontal (PF) cortex neurons distinguishes short from long time intervals. Here, we examined whether this property reflected a general timing mechanism or one dependent on behavioral context. In one task, monkeys discriminated the relative duration of 2 stimuli; in the other, they discriminated the relative distance of 2 stimuli from a fixed reference point. Both tasks had a pre-cue period (interval 1) and a delay period (interval 2) with no discriminant stimulus. Interval 1 elapsed before the presentation of the first discriminant stimulus, and interval 2 began after that stimulus. Both intervals had durations of either 400 or 800 ms. Most PF neurons distinguished short from long durations in one task or interval, but not in the others. When neurons did signal something about duration for both intervals, they did so in an uncorrelated or weakly correlated manner. These results demonstrate a high degree of context dependency in PF time processing. The PF, therefore, does not appear to signal durations abstractedly, as would be expected of a general temporal encoder, but instead does so in a highly context-dependent manner, both within and between tasks.

We introduce the -1 dual Hahn polynomials through an appropriate $q \to -1$ limit of the dual q-Hahn polynomials. These polynomials are orthogonal on a finite set of discrete points on the real axis, but in contrast to the classical orthogonal polynomials of the Askey scheme, the -1 dual Hahn polynomials do not exhibit the Leonard duality property. Instead, these polynomials satisfy a 4-th order difference eigenvalue equation and thus possess a bispectrality property. The corresponding generalized Leonard pair consists of two matrices $A,B$ each of size $N+1 \times N+1$. In the eigenbasis where the matrix $A$ is diagonal, the matrix $B$ is 3-diagonal; but in the eigenbasis where the matrix $B$ is diagonal, the matrix $A$ is 5-diagonal.

Summary Background Both obesity and left ventricular (LV) diastolic dysfunction are associated with an increased risk of cardiovascular morbidity and mortality. There is a paucity of data as to whether obesity is independently associated with LV diastolic dysfunction. Methods Adult patients with sinus rhythm referred for a transthoracic echocardiography between July, 2007, and December, 2007, were prospectively included. Exclusion criteria were patient who had a history of congenital or valvular heart disease, treatment with pacemaker implantation or implantable cardioverter defibrillator, myocardial infarction, or impaired LV systolic function. Diastolic function was classified by an algorithm incorporating data from mitral and pulmonary venous flow indices, and Doppler tissue imaging. Body mass index (BMI) was evaluated as a categorical variable (normal weight 2 ; overweight 25.0 to 2 ; and obese ≥30kg/m 2 ). Logistic models were used to assess the risk of abnormal LV diastolic function associated with BMI categories. Results Of a total number of 692 patients who met all study criteria (mean 59±15year-old; 50% women, 48% hypertension, 16% diabetes, 26% overweight, 8% obese), 538 (78%) had abnormal LV diastolic function. In multivariate analyses adjusting for age, sex, and cardiovascular risk factors, obesity was independently associated with LV diastolic dysfunction (odds ratio [OR]: 2.98, 95% confidence interval [CI]: 1.12–7.88; P =0.03) compared to normal weight. LV mass did not weaken this association (OR: 2.88, 95% CI: 1.08–7.68; P =0.04). Overweight was not independently associated with LV diastolic dysfunction. Conclusion Obesity was associated with LV diastolic dysfunction independent of cardiovascular risk factors and LV mass.

Pioglitazone has been shown to reduce the occurrence of fatal and nonfatal myocardial infarction (MI) in type 2 diabetes mellitus (DM). However, the mechanisms of such favorable effects remain speculative. The aim of this study was to investigate the effect of pioglitazone on arterial baroreflex sensitivity (BRS) and muscle sympathetic nerve activity (MSNA) in 30 DM patients with recent MI. Patients were randomly assigned to those taking pioglitazone (n = 15) and those not taking pioglitazone (n = 15) at 4 weeks after the onset of MI. BRS, MSNA, calculated homeostasis model assessment of insulin resistance index (HOMA-IR), and plasma adiponectin were measured at baseline and after 12 weeks. Pioglitazone increased plasma adiponectin (from 6.9 ± 3.3 μg/dL to 12.2 ± 7.1 μg/dL) and reduced HOMA-IR (from 4.0 ± 2.2 to 2.1 ± 0.9). In the pioglitazone group, MSNA decreased significantly (from 37 ± 7 bursts/min to 25 ± 8 bursts/min) and BRS increased significantly (from 6.7 ± 3.0 to 9.9 ± 3.2 ms/mm Hg) after 12 weeks. Furthermore, a significant relationship was found between the change in MSNA and HOMA-IR (r = 0.6, P = 0.042). Thus, pioglitazone decreased the sympathetic nerve traffic through the improvement of insulin resistance in DM patients with recent MI, which indicate that the sympathoinhibitory effects of pioglitazone may, at least in part, have contributed to the beneficial effects of pioglitazone.

We consider the most general Dunkl shift operator L with the following properties: (i) L is of first order in the shift operator and involves reflections; (ii) L preserves the space of polynomials of a given degree; (iii) L is potentially self-adjoint. We show that under these conditions, the operator L has eigenfunctions which coincide with the Bannai–Ito polynomials. We construct a polynomial basis which is lower-triangular and two-diagonal with respect to the action of the operator L. This allows to express the BI polynomials explicitly. We also present an anti-commutator AW(3) algebra corresponding to this operator. From the representations of this algebra, we derive the structure and recurrence relations of the BI polynomials. We introduce new orthogonal polynomials – referred to as the complementary BI polynomials – as an alternative q → − 1 limit of the Askey–Wilson polynomials. These complementary BI polynomials lead to a new explicit expression for the BI polynomials in terms of the ordinary Wilson polynomials.

When we encode faces in memory, we often do so in association with biographical information regarding the person. To examine the neural dynamics underlying such encoding processes, we devised a face recognition task and recorded cortical activity using magnetoencephalography. The task included two conditions. In the experimental condition, face stimuli were preceded by biographical information regarding the person whose face was to be memorized, whereas in the control condition, nonsense syllables were presented before face stimuli. Behavioral results indicated that the biographical information about a person facilitated the recognition memory of their face. Magnetoencephalography signals showed clear visually evoked magnetic fields mainly in the occipitotemporal cortex, in response to the face stimuli that were to be encoded. The phasic peak was observed at 100-200 ms after onset of a face stimulus, which was followed by late latency deflections (200-400 ms). Comparison of the signal between conditions revealed that the preceding semantic information does modulate the neuromagnetic responses to the face stimuli. This modulation occurred primarily at the late latency component in the sensors over the occipitotemporal cortex. In addition, the effects of conditions were also observed in the signals from more anterior sensors, which occurred earlier than the effects in the occipitotemporal cortex. These results provide insights into the neural dynamics underlying the encoding of faces in association with their biographical information.

Left atrial (LA) enlargement has been acknowledged as a significant predictor of cardiovascular morbidity and mortality.To evaluate the accuracy of two-dimensional and three-dimensional echocardiography for determining LA volume, LA volume measurements by echocardiography were compared with those measured by 64-slice multidetector computed tomography (MDCT) as a reference standard.Fifty-seven consecutive patients (mean age, 66 ± 11 years; 59% men) referred to echocardiography and MDCT on the same day were prospectively evaluated. LA volume by three-dimensional echocardiography was correlated closely with that by MDCT (r = 0.95, P.0001), with 8% underestimation. LA volume by two-dimensional echocardiography was correlated less well with that measured by MDCT (r = 0.86, P.0001) and consistently underestimated LA volume by 19%, particularly as the left atrium enlarged.LA volume assessment by three-dimensional echocardiography was correlated closely with that measured by MDCT, albeit with an 8% underestimation. Three-dimensional echocardiography is a feasible noninvasive method to evaluate LA volume.

Contrast-induced nephropathy (CIN) is associated with increased morbidity and mortality rates. Although a previous study reported that pretreatment with sodium bicarbonate is more effective than sodium chloride for prophylaxis of CIN, this has not been a universal finding. We performed a prospective randomized trial to investigate whether CIN can be avoided using sodium bicarbonate. In total 155 patients with a glomerular filtration rate (GFR)

A patient without any known congenital cardiac abnormalities who suffered from ventricular tachycardia was taken to the emergency room following successful resuscitation. Transthoracic echocardiography showed diffuse left ventricle dysfunction and mild aortic regurgitation. Coronary angiography demonstrated intact coronary and suspected morphological abnormalities of the aortic valve. In addition, transesophageal echocardiography revealed a rare quadricuspid aortic valve malformation. After controlling ventricular tachycardia and congestive heart failure with optimal medical therapy, the patient had an uneventful course and was subsequently discharged 3 weeks after admission. To our knowledge, this is the first report of quadricuspid aortic valve associated with idiopathic dilated cardiomyopathy.

It is shown that the nonautonomous discrete Toda equation and its Backlund transformation can be derived from the reduction of the hierarchy of the discrete KP equation and the discrete two-dimensional Toda equation. Some explicit examples of the determinant solutions of the nonautonomous discrete Toda equation including the Askey-Wilson polynomial are presented. Finally we discuss the relationship between the nonautonomous discrete Toda system and the nonautonomous discrete Lotka-Volterra equation.

The frontal pole cortex (FPC) expanded markedly during human evolution, but its function remains uncertain in both monkeys and humans. Accordingly, we examined single-cell activity in this area. On every trial, monkeys decided between two response targets on the basis of a 'stay' or 'shift' cue. Feedback followed at a fixed delay. FPC cells did not encode the monkeys' decisions when they were made, but did so later on, as feedback approached. This finding indicates that the FPC is involved in monitoring or evaluating decisions. Using a control task and delayed feedback, we found that decision coding lasted until feedback only when the monkeys combined working memory with sensory cues to 'self-generate' decisions, as opposed to when they simply followed trial-by-trial instructions. A role in monitoring or evaluating self-generated decisions could account for FPC's expansion during human evolution.

SummaryWe examined activity in the frontal cortex as monkeys performed a duration-discrimination task. Two stimuli, one red and the other blue, appeared sequentially on a video screen—in either order. Later, both stimuli reappeared, and to receive a reward the monkeys had to choose the stimulus that had lasted longer during its initial presentation. Some neurons encoded stimulus duration, but a larger number of cells represented their relative duration, which was encoded in three ways: whether the first or second stimulus had lasted longer; whether the red or blue stimulus had lasted longer; or, less commonly, as the difference between the two durations. As the monkeys' choice approached, the signal encoding which stimulus (red or blue) had lasted longer increased as the order-based signal dissipated. By representing stimulus durations and relative durations—both bound to stimulus features and event order—the frontal cortex could contribute to both temporal perception and episodic memory.

The primate prefrontal cortex contributes to stimulus-guided behavior, but the functional specializations among its areas remain uncertain. To better understand such specializations, we contrasted neuronal activity in the dorsolateral prefrontal cortex (PFdl) and the orbital prefrontal cortex (PFo). The task required rhesus monkeys to use a visual cue to choose a saccade target. Some cues instructed the monkeys to repeat their most recent response; others instructed them to change it. Responses were followed by feedback: fluid reward if correct, visual feedback if incorrect. Previous studies, using different tasks, have reported that PFo neurons did not encode responses. We found PFo did encode responses in this task, but only near feedback time, after the response had been completed. PFdl differed from PFo in several respects. As reported previously, some PFdl neurons encoded responses from the previous trial and others encoded planned responses. PFo neurons did not have these properties. After feedback, PFdl encoded rewarded responses better than unrewarded ones and thus combined response and outcome information. PFo, in contrast, encoded the responses chosen, rewarded or not. These findings suggest that PFdl and PFo contribute differently to response knowledge, with PFo using an outcome-independent signal to monitor current responses at feedback time.

We consider a difference-difference Davey-Stewartson system together with its bilinear structure. We write some new Gram-type determinantal solutions taking into account a set of Jacobi identities for determinants. A bilinear Backlund transformation is constructed and consequently a Lax pair for the discrete system is derived.

We studied single-neuron activity in the monkey dorsolateral prefrontal cortex during a saccade task, in which correct responses were rewarded after a delay of 0.5 or 1.5 s in one trial-block, and after 1.5 or 3-s delay in the other trial-block. Activity of some neurons depended on the relative length of the delays (longer or shorter) within each block, and activity for the 1.5-s trials was significantly different between the blocks. Activity of another group of neurons reflected the absolute length of delay: hence, the activity in the 1.5-s trials did not differ between the blocks. These results indicate that both relative and absolute time of future reward is represented in subsets of neurons in the dorsolateral prefrontal cortex.

The notion of Frobenius-Stickelberger-Thiele (FST) polynomials is introduced. Spectral transformations for these polynomials analogous to the Christoffel and Geronimus transformations for orthogonal polynomials are constructed. They yield an integrable discrete time chain (the FST chain) related to the generalized e-algorithm. Relations of the FST polynomials to the Pade interpolation problem and to general and symmetric biorthogonal rational functions are considered in detail.

The lateral prefrontal cortex (LPFC) plays a major role in both working memory (WM) and response inhibition (RI), which are fundamental for various cognitive abilities. We explored the relationship between these LPFC functions during childhood development by examining the performance of two groups of children in visuospatial and auditory WM tasks and a go/no-go RI task. In the younger children (59 5- and 6-year-olds), performance on the visuospatial WM task correlated significantly with that in the auditory WM task. Furthermore, accuracy in these tasks correlated significantly with performance on the RI task, particularly in the no-go trials. In contrast, there were no significant correlations among those tasks in older children (92 8- and 9-year-olds). These results suggest that functional neural systems for visuospatial WM, auditory WM, and RI, especially those in the LPFC, become fractionated during childhood, thereby enabling more efficient processing of these critical cognitive functions.

Backgound: Left atrial (LA) enlargement has been proposed as a barometer of diastolic dysfunction and a predictor of congestive heart failure (CHF) in patients with sinus rhythm. Whether LA volume predicts CHF in patients with atrial fibrillation (AF) is not well known. Methods: To determine the clinical importance of LA volume in the prediction of CHF in patients with AF, AF patients referred for clinically-indicated echocardiogram, without a history of significant mitral valve disease, congenital heart disease, pacemaker, or cardiac surgery, in 2007-2008 were prospectively included and followed forward them up to September 2014. LA volume was measured using the biplane area-length formula. CHF was ascertained using the Framingham criteria. Cox proportional hazards modeling was used to assess the risk factors of CHF development. Results: Of 456 AF patients who met all study criteria (mean 70 ± 10 year-old, 67% men, 62% hypertension, 26% diabetes, LV ejection fraction 68 ± 13%, LA volume 52 ± 24 mL/m 2 ), 46 (10%) developed CHF events during a mean follow-up of 44 ± 31 months. CHF events were significantly increased with advancing age (HR 1.4, 95%CI 1.0-2.0, P2 ; HR 1.2, 95% CI 1.1-1.3, P Conclusions: In our cohort with AF, LA volume predicted CHF developments, independent of LV systolic function and other cardiovascular comorbidities, which appears to be clinically useful information for risk stratification.

Rhesus monkeys performed two tasks, both requiring a choice between a red square and a blue circle. In the duration task, the two stimuli appeared sequentially on each trial, for varying durations, and, later, during the choice phase of the task, the monkeys needed to choose the one that had lasted longer. In the matching-to-sample task, one of the two stimuli appeared twice as a sample, with durations matching those in the duration task, and the monkey needed to choose that stimulus during the choice phase. Although stimulus duration was irrelevant in the matching-to-sample task, the monkeys made twice as many errors when the second stimulus was shorter. This across-task interference supports an order-dependent model of the monkeys' choice and reveals something about their strategy in the duration task. The monkeys tended to choose the second stimulus when its duration exceeded the first and to choose the alternative stimulus otherwise. For the duration task, this strategy obviated the need to store stimulus-duration conjunctions for both stimuli, but it generated errors on the matching-to-sample task. We examined duration coding in prefrontal neurons and confirmed that a population of cells encoded relative duration during the matching-to-sample task, as expected from the order-dependent errors.

An 84-year-old woman undergoing maintenance hemodialysis presented with chest discomfort lasting several days and electrocardiographic abnormalities. She had stopped smoking 2 weeks earlier and was experiencing irritability. Upon admission, electrocardiography showed ST-segment elevation in leads I, II, aVF, and V2-6 and an abnormal Q wave in leads II, III, and aVF. Ultrasound cardiography showed left ventricular anteroapical akinesia and basal hyperkinesia. The chest discomfort disappeared without specific therapy. During hospital days 1-5, the ST-segment elevation gradually improved. Giant negative T waves then developed. The left ventricular asynergy resolved by day 8. Radionuclide imaging with iodine-123-beta-methyl-p-iodophenyl pentadecanoic acid, but not with technetium-99 m-sestamibi, showed an apical defect. Elective coronary angiography showed no stenosis. 'Takotsubo' cardiomyopathy was diagnosed. After discharge, the patient continued regular dialysis without cardiac symptoms. We concluded that endogenously activated sympathetic nerve action in hemodialysis patients, especially those under emotional or physical stress, might be a causative factor for Takotsubo cardiomyopathy.

The integrable chain of RII type by Spiridonov–Zhedanov is studied by using the bilinear method. Bilinear equations of the system are derived by applying appropriate-dependent variable transformations. A particular solution on a semi-infinite lattice is explicitly given in terms of the Casorati-type determinants. It is shown that the RII chain and the Toda-type integrable systems are connected by Backlund transformations.

A $q$ -discrete analog of the Toda molecule equation and its $N$ -soliton solution are constructed by using the bilinear method. The solution is expressed in the Casorati determinant form whose elements are given in terms of the $q$ -orthogonal polynomials.

Temporal prediction of future events, especially regarding reward delivery, is critical for controlling/learning purposeful behavior. The dorsolateral prefrontal cortex (DLPFC) has been considered to be involved in behavioral control based on prospective coding for future events, including reward. Thus this area is likely to have a neuronal mechanism responsible for temporal prediction of forthcoming reward. To address this hypothesis, we recorded the neuronal activity from the DLPFC of macaque monkeys while they performed an oculomotor delayed-response task under two conditions regarding the time of reward delivery. In this task, when the subjects made a correct response, the reward was delivered after a reward-delay period of 0.5 or 2 s. At the behavioral level, the onset latency for saccades was significantly faster in the shorter reward-delay trials (0.5 s) than in longer reward-delay trials (2 s), indicating that our subjects actually predicted the time of reward delivery. At the neuronal level, we found that many DLPFC neurons showed differential activity depending on the predicted time of reward delivery during the cue and/or delay periods. These results suggest that a fraction of neurons in the DLPFC represent the temporal prediction of reward and probably a variety of other future events.