Development of absolute thresholds in chickens

Absolute auditory thresholds were estimated in chickens at 0 and 4 days after hatching. Momentary suppressions of the chicks' regular peeping, following the onset of a tone, were used as indications of stimulus detection. In the first experiment a staircase procedure was used to estimate thresholds. The absolute thresholds of both ages were the same at low frequencies (250-500 Hz), but at higher frequencies (1-2 kHz) 4-day-old chicks had lower thresholds than the 0-day-old chicks. The estimates of thresholds at 1 kHz were corroborated in the second experiment with a method of constant stimuli. A more efficient modified method of limits was used to replicate the age by frequency interaction in the third experiment. These changing thresholds are likely to reflect a developmental process somewhere in the auditory system and not some nonsensory artifact for two reasons: similar thresholds at low frequencies show that developmental differences are not due to differences in the sensitivity of the testing procedure at the two ages and thresholds obtained from the 4-day-old birds are similar to estimates from mature birds. In conclusion, responsiveness to low frequencies develops before responsiveness to higher frequencies, showing that the development of absolute thresholds is correlated with other measures of functional maturation in the auditory system.     

The Max-Flow Min-Cut theorem for countable networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.     

Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid stochastic differential equations

This is a continuation of the first author’s earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [1] is the global Lipschitz condition. However, we will show in this paper that without this global Lipschitz condition the EM method may not preserve the almost sure exponential stability. We will then show that the backward EM method can capture the almost sure exponential stability for a certain class of highly nonlinear hybrid SDEs.     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Independent systems of representatives in weighted graphs

The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set of a graph with maximal degree Δ is partitioned into sets V _i of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V _i at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell, on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of ISR’s. The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion. The research of the third author was supported by the Sacta-Rashi Foundation.     

Spectral-Null Codes and Null Spaces of Hadamard Submatrices

Codes of length 2 ^m over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of all have an rth order spectral null at zero frequency. Establishing the connection between and the parity-check matrix of Reed-Muller codes, the minimum distance of is obtained along with upper bounds on the redundancy of . An efficient algorithm is presented for encoding unconstrained binary sequences into .     

Studies of Hindered Rotation and Magnetic Anisotropy by 1H, 13C and 19F NMR. The Diels-Alder Adduct of N- Pentafluorophenylmaleimide and Phencyclone: A Model for Drugs.

The potent Diels-Alder diene, phencyclone, 1, reacts with N-pentafluorophenylmaleimide, 2, to form an adduct, 3, characterized by ¹H, ¹³C, and ¹⁹F NMR at 300, 75 and 282 MHz, respectively. The one-dimensional (1D) and two-dimensional (2D) ¹H and ¹³C NMR spectra of 3 at ambient temperatures imply a slow exchange limit (SEL) regime with respect to rotation of the unsubstituted bridgehead phenyl groups about severely hindered C(sp²)-C(sp³) bonds. Major non-bonded interactions are expected between the ortho protons of the C₆H₅ groups and H-1, 8 of the phenanthrenoid moiety of 3. ¹⁹F 1D and 2D (COSY) NMR spectra show that the SEL regime also obtains for rotation about the N-C₆F₅ bond of 3, with five separate fluorine signals seen, consistent with a preferred conformation in which the C₆F₅ may lie roughly perpendicular to the plane of the pyrrolidinedione moiety, and may be in the mirror symmetry plane of 3. The results are considered relevant to hindered aryl rotations in numerous Pharmaceuticals. Selected spectral data for 2 and precursors are also presented.     

A Review of the Integration of Science and Mathematics: Implications for Further Research

Building on the earlier analysis by Berlin (1991) , this paper reviews various studies on integrating mathematics and science in the 1990s and provides some implications for further research. The areas identified for further exploration include comparison of the nature of mathematics and science, epistemological debates in mathematics and in science education, the bases used to emphasize science over mathematics or vice versa, empirical evidence of effectiveness of integration, connections between teacher education programs for integration and teachers' subsequent classroom teaching practices, perceptions of integration on the part of teacher educators, contextual difficulties in implementing integrated approaches and possible solutions, and rationales of integrating mathematics and science through technology. In order to help all students become scientifically literate, which most reform documents call for, more focused attention on integration of curriculum and instruction is necessary.     

Simulating the Performance of Michelson- and Sagnac-based Laser Interferometric Gravitational Wave Detectors in the Presence of Mirror Tilt and Curvature Errors

We model the behaviour of single-bounce delay-line dual recycled Sagnac-based interferometer and compare its performance with that of single-bounce Michelson-based system. Geometric imperfections such as mirror tilt and curvature mismatch can strongly influence the performance of the Sagnac device due to the inherently smaller free spectral range (FSR) and higher order mode spacing. This leads to a greater number of higher order modes near, or within the signal band in the signal recycling cavity of the instrument. The important consequence of that is, in general, a greater sensitivity of a Sagnac system to nonideal parameters and imperfections of various kind affecting the performance of a real interferometer. A number of optical configurations have also been examined numerically to determine the best possible optical arrangement, in the presence of such geometric imperfections. We show that there is an optimum choice for the nominal radius of curvature of the end mirrors which results from balancing the loss due to mirror tilt against that due to curvature mismatch.     

Impaired pulmonary blood flow distribution in congestive heart failure assessed using synchrotron radiation microangiography

Synchrotron radiation microangiography is a powerful tool for assessing adverse changes in pulmonary vessel density associated with primary pulmonary hypertension (PH). Congestive heart failure (CHF) leads to a `secondary' onset of PH, yet it is unknown whether secondary PH is also associated with reduced vessel density. This study utilized synchrotron radiation to assess both pulmonary vessel density and endothelial function in a Dahl rat model of CHF with secondary PH. High salt‐fed Dahl salt‐sensitive (Dahl‐S) and salt‐resistant (Dahl‐R) rats were anesthetized and microangiography was performed to assess the pulmonary vessel density and vascular responses to (i) sodium nitroprusside (5.0 µg kg^?1 min^?1), (ii) acetylcholine (3.0 µg kg^?1 min^?1) and (iii) ET‐1_A receptor blockade, BQ‐123 (1 mg kg^?1). Dahl‐S rats developed CHF and secondary PH as evident by endothelial dysfunction, impaired vasodilatory responses to acetylcholine, enhanced vasodilatory responses to BQ‐123 and extensive pulmonary vascular remodeling. Consequently, the pulmonary vessel density was adversely reduced. Interestingly, the etiology of secondary PH manifests with structural and functional changes that are comparable with that previously reported for primary PH. One important discrepancy, however, is that ET‐1 modulation of pulmonary vessels is most striking in vessels with a diameter range of 100–200 µm in secondary PH, in contrast to a range of 200–300 µm in primary PH. Such discrepancies should be considered in future studies investigating primary and secondary forms of PH.