Explicit Pairs Research Articles

Application of explicit Hilbert's pairing to constructive class field theory and cryptography

Application of explicit Hilbert's pairing to constructive class field theory and cryptography

Painlevé Representation of Tracy–Widom $${_\beta}$$ β Distribution for $${\beta}$$ β = 6

In arXiv:1306.2117, we found explicit Lax pairs for the soft edge of beta ensembles with even integer values of $\beta$. Using this general result, the case $\beta=6$ is further considered here. This is the smallest even $\beta$, when the corresponding Lax pair and its relation to Painlev\'e II (PII) have not been known before, unlike cases $\beta=2$ and $4$. It turns out that again everything can be expressed in terms of the Hastings-McLeod solution of PII. In particular, a second order nonlinear ODE for the logarithmic derivative of Tracy-Widom distribution for $\beta=6$ involving the PII function in the coefficients, is found, which allows one to compute asymptotics for the distribution function. The ODE is a consequence of a linear system of three ODEs for which the local singularity analysis yields series solutions with exponents in the set $4/3$, $1/3$ and $-2/3$.

Intrusion Detection using Ensemble Learning on Combined Features

Network intrusions may illicitly retrieve data/information, or prevent legitimate access. Reliable detection of network intrusions is an important problem, misclassification of an intrusion is an issue by the resultant overall reduction of accuracy of detection. A variety of potential methods exist to develop an improved system to perform classification more accurately. Feature selection is one area that may be utilized to successfully improve performance by initially identifying sets and subsets of features that are relevant and non-redundant. Within this paper explicit pairings of features have been investigated in order to determine if the presence of pairings has a positive effect on classification, potentially increasing the accuracy of detecting intrusions correctly. In particular, classification using the ensemble algorithm, StackingC, with F-Measure performance and derived Information Gain Ratio, as well as their subsequent correlation as a combined measure, are presented.

Gauge theories and dessins d’enfants: beyond the torus

Dessin d'Enfants on elliptic curves are a powerful way of encoding doubly-periodic brane tilings, and thus, of four-dimensional supersymmetric gauge theories whose vacuum moduli space is toric, providing an interesting interplay between physics, geometry, combinatorics and number theory. We discuss and provide a partial classification of the situation in genera other than one by computing explicit Belyi pairs associated to the gauge theories. Important also is the role of the Igusa and Shioda invariants that generalise the elliptic $j$-invariant.

Cross effects and calculus in an unbased setting

We study functors F from C_f to D where C and D are simplicial model categories and C_f is the full subcategory of C consisting of objects that factor a fixed morphism f from A to B. We define the analogs of Eilenberg and Mac Lane's cross effects functors in this context, and identify explicit adjoint pairs of functors whose associated cotriples are the diagonals of the cross effects. With this, we generalize the cotriple Taylor tower construction of [10] from the setting of functors from pointed categories to abelian categories to that of functors from C_f to D to produce a tower of functors whose n-th term is a degree n functor. We compare this tower to Goodwillie's tower of n-excisive approximations to F found in [8]. When D is a good category of spectra, and F is a functor that commutes with realizations, the towers agree. More generally, for functors that do not commute with realizations, we show that the terms of the towers agree when evaluated at the initial object of C_f.

Feel Effects

Despite a long history of use in communication, haptic feedback is a relatively new addition to the toolbox of special effects. Unlike artists who use sound or vision, haptic designers cannot simply access libraries of effects that map cleanly to media content, and they lack even guiding principles for creating such effects. In this article, we make progress toward both capabilities: we generate a foundational library of usable haptic vocabulary and do so with a methodology that allows ongoing additions to the library in a principled and effective way. We define a feel effect as an explicit pairing between a meaningful linguistic phrase and a rendered haptic pattern. Our initial experiment demonstrates that users who have only their intrinsic language capacities, and no haptic expertise, can generate a core set of feel effects that lend themselves via semantic inference to the design of additional effects. The resulting collection of more than 40 effects covers a wide range of situations (including precipitation, animal locomotion, striking, and pulsating events) and is empirically shown to produce the named sensation for the majority of our test users in a second experiment. Our experiments demonstrate a unique and systematic approach to designing a vocabulary of haptic sensations that are related in both the semantic and parametric spaces.

Gap Probabilities for the Generalized Bessel Process: A Riemann-Hilbert Approach

We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case, a determinantal process which arises as critical limiting kernel in the study of self-avoiding squared Bessel paths. We prove that such gap probabilities, i.e. the scalar and matrix Fredholm determinant of the process respectively, can be expressed in terms of determinants of suitable Its-Izergin-Korepin-Slavnov integrable kernels and therefore they can be related in a canonical way to Riemann-Hilbert problems. Moreover, such Fredholm determinants can be interpreted as isomonodromic τ-functions in the sense of Jimbo, Miwa and Ueno; in particular, in the single-time case we are able to construct an explicit Lax pair. On the other hand, in the multi-time case we explicitly define a completely new multi-time kernel and we proceed with the study of gap probabilities as in the single-time case.

Controllability of the 1D Schrödinger equation by the flatness approach

We derive in a straightforward way the exact controllability of the 1-D Schrödinger equation with a Dirichlet boundary control. We use the so-called flatness approach, which consists in parameterizing the solution and the control by the derivatives of a “flat output”. This provides an explicit control input achieving the exact controllability in the energy space. As an application, we derive an explicit pair of control inputs achieving the exact steering to zero for a simply-supported beam.

Effects of national identity salience on responses to ads

This paper investigates the effect of national identity salience on responses to ads in two contexts: national identity activated through media context, and national identity activated through advertising appeals. The results remain consistent with the idea that heightening national identity leads individuals to react more positively to representations of that identity. The salience manipulations serve to influence respondents' evaluations of ads and purchase intentions. Respondents present more favorable evaluations of ads and intentions to purchase the advertised products when the ads explicitly pair the advertised product with national identity symbols or rhetoric, as compared to when no such explicit pairing occurs. Further, the activation of individuals' national identity through media context affects the response to embedded ads, even when those ads do not explicitly pair the product with national symbols or rhetoric.

Optimal Fixed Gain Linear Processing for Amplify-and-Forward Multichannel Relaying

In this correspondence, we consider the problem of linear processing design at the relay for amplified-and-forward relaying in a multichannel system. Assuming a fixed-gain power amplification at the relay, we study the linear processing structure to maximize the end-to-end achievable rate. For both the cases of relaying with or without direct path, we show that the optimal unitary processing matrix is of permutation structure, i.e., channel pairing is optimal. Furthermore, in each case, the explicit optimal channel pairing strategy is obtained based on sorting certain function of received SNR over the incoming and outgoing subchannels. This result is especially noticeable for the case with direct path, where the optimal linear processing was not known before under any power allocation. Specifically, we show that the pairing is according to the ordering of the relative SNR ratio on a subchannel over first hop to its direct path, and that of SNR strengths on subchannels over the second hop. Simulation results are presented to demonstrate the achievable gain of optimal channel pairing over non-optimal linear processing or no-pairing cases. It is also shown that the performance of channel pairing under the simple fixed-gain power allocation outperforms that under the traditional uniform power allocation.

Topologicald-wave pairing structures in Jain states

We discuss d-wave topological (broken time reversal symmetry) pairing structures in unpolarized and polarized Jain states. We demonstrate pairing in the Jain spin singlet state by rewriting it in an explicit pairing form, in which we can recognize d-wave weak pairing of underlying quasiparticles - neutral fermions. We find and describe the root configuration of the Jain spin singlet state and its connection with neutral excitations of the Haldane-Rezayi state, and study the transition between these states via exact diagonalization. We find high overlaps with the Jain spin singlet state upon a departure from the hollow core model for which the Haldane-Rezayi state is the exact ground state. Due to a proven algebraic identity we were able to extend the analysis of topological d-wave pairing structures to polarized Jain states and integer quantum Hall states, and discuss its consequences.

Equal modal damping design for a family of resonant vibration control formats

The principle of equal modal damping is used to give a unified presentation and calibration of resonant control of structures for different control formats, based on velocity, acceleration–position or position feedback. When introducing a resonant controller the original resonant mode splits into two, and if these are required to have the same modal damping ratio, the characteristic equation conforms to a two-parameter format. By selecting a suitable relative separation of the modal frequencies, the design problem defines a one-parameter family – determined, for example, in terms of the resulting modal damping ratio. While velocity feedback, and the associated acceleration–position formats, lead to near-equal resonant peak heights of the velocity in a frequency response diagram, position feedback leads to balanced acceleration peaks. It is demonstrated, how a simple additional time derivative term in the control coupling can change these properties into balanced position and velocity peaks, respectively. In particular this gives an improved control format based on measurement of structural displacement or deformation. In all cases the optimal calibration in terms of a root locus identification leads to a simple explicit pair of design formulae for controller frequency and damping ratio based on a simple two -degrees-of-freedom system. Unconditional stability is demonstrated for a general multi-degrees-of-freedom system with multiple controllers for the velocity and acceleration-velocity formats, while the position and extended position feedback format give a simple stability condition in terms of the gain factors and the structure flexibility matrix. The paper concludes with a simple design procedure based on the desired effective damping of a flexible structure with equal modal control in any of the discussed resonant formats.

Algebraic structures on double and plane posets

We study the Hopf algebra of double posets and two of its Hopf subalgebras, the Hopf algebras of plane posets and of posets without N. We prove that they are free, cofree, self-dual, and we give an explicit Hopf pairing on these Hopf algebras. We also prove that they are free 2-As algebras; in particular, the Hopf algebra of posets without N is the free 2-As algebra on one generator. We deduce a description of the operads of 2-As algebras and of B ? algebras in terms of plane posets.

Using Ketamine to Model Semantic Deficits in Schizophrenia

Semantic deficits constitute a core cognitive abnormality in schizophrenia. In the current study, the N-methyl-d-aspartate receptor antagonist ketamine was administered to healthy individuals acutely while they performed semantic processing tasks that included word pairs of differing degrees of semantic relatedness. Two dimensions of semantic processing were investigated: (1) explicit versus implicit processing, that is, unconscious versus conscious processing of semantic relationships and (2) direct versus indirect processing, that is, word pairs that are closely (LION-TIGER) or distantly (LION-STRIPES) related. The immediate effects of ketamine (0.8 mg/kg per hour during 80 minutes with approximate target plasma levels of 200 ng/mL) were examined in a placebo-controlled double-blind repeated-measures group design with 19 participants. It was predicted that ketamine would disrupt access to semantic memory as evidenced in schizophrenia, especially the indirectly related word pairs. In addition, implicit processing and explicit processing were predicted to be differentially affected. Ketamine administration did result in an abnormal performance in the reaction time responses to implicitly presented indirectly related word pairs (ie, greater priming) and reduced accuracy for explicit pairs. Performance on the directly related word pair tasks (both implicit and explicit) was similar across ketamine and placebo conditions, except for the suggestion of abnormal semantic matching in the accuracy data in the implicit task. This study confirms that implicit indirect semantic processing is changed under the influences of ketamine akin to schizophrenia. Future research comparing a schizophrenia group and a ketamine group directly about these tasks is needed to determine the similarity of impairments.

Numerical study of DNA-functionalized microparticles and nanoparticles: Explicit pair potentials and their implications for phase behavior

DNA-coated colloids have great potential for the design of complex self-assembling materials. In order to predict the structures that will form, knowledge of the interactions between DNA-functionalized particles is crucial. Here, we report results from Monte Carlo simulations of the pair-interaction between particles coated with single-stranded DNA sticky ends that are connected to the surface by relatively short and stiff surface tethers. We complement our calculations with a study of the interaction between two planar surfaces coated with the same DNA. Based on our simulations we propose analytical expressions for the interaction potentials. These analytical expressions describe the DNA-mediated interactions well for particle sizes ranging from tens of nanometers to a few micrometers and for a wide range of grafting densities. We find that important contributions to both the repulsive and attractive parts of the free energy come from purely entropic effects of the discrete tethered sticky ends. Per bond, these entropic contributions have a magnitude similar to the hybridization free energy of a free pair of sticky ends in solution and they can thus considerably change the effective sticky-end binding strength. Based on the calculated interaction potentials, we expect that stable gas-liquid separation only occurs for particles with radii smaller than a few tens of nanometers, which suggests that nanoparticles and micrometer-sized colloids will follow different routes to crystallization. Finally, we note that the natural statistical nonuniformities in the surface distribution of sticky ends lead to large variations in the binding strength. This phenomenon may compromise the reliability of tests that aim to detect specific DNA targets in diagnostics. In addition to guiding the design of novel self-assembling materials and gene-detection assays, the insights presented here could also shed more light on (multivalent) interactions in other systems with tethered binding groups, for instance in the areas of supramolecular chemistry or ligand-receptor mediated biorecognition.

Sensitivity analyses of a precerebellar neuron model predict a morphologic mechanism for plasticity of neuronal function

The vestibuloocular reflex (VOR) provides an amenable model of learning and memory. Neurons from the Area II nucleus of goldfish are necessary for VOR plasticity, carrying an efferent copy of the eye velocity motor command to the cerebellum. Recently we introduced a novel sensitivity analysis method [1] to quantify how dendritic morphology and intrinsic electrical parameters affect neuronal function. This approach also allows precise combinations of active conductances to be predicted that can compensate for a given morphologic change to restore normal function. Here we have extended our method to analyze interactions between explicit pairs of parameters. We reconstructed the morphology and built multi-compartment models of three distinct Area II neurons, followed by an automated parameter optimization to fit each model to a single set of physiological data. Using partial least squares regression to identify sensitivity trends globally across the space of active and morphologic parameters, neuronal outputs relevant to eye velocity integration were found to be driven largely by intracellular calcium concentration near the soma, and voltage attenuation in distal dendrites. We then analyzed the second order sensitivity matrices (Hessians) of perisomatic calcium concentration and distal voltage attenuation, for each morphologic model at two disparate points in parameter space. The results identified sensitive directions, precise combinations of electrical and morphologic parameters that varied output the most, and robust directions that varied output the least. Perturbing the model along the sensitive direction of distal voltage attenuation, which minimally changed perisomatic calcium concentration, was sufficient to induce functional changes that might underlie vestibular plasticity paradigms. Yet, even large perturbations along the robust direction of distal voltage attenuation had little effect on functional output. Our results show that specific, subtle changes of morphology and conductances in the dendrites are sufficient to alter the range of a neuron’s firing dynamics. We propose that dendritic morphology plays a significant role in determining the functional flexibility, or robustness, of a neuron.

New embedded explicit pairs of exponentially fitted Runge–Kutta methods

Two new embedded pairs of exponentially fitted explicit Runge–Kutta methods with four and five stages for the numerical integration of initial value problems with oscillatory or periodic solutions are developed. In these methods, for a given fixed ω the coefficients of the formulae of the pair are selected so that they integrate exactly systems with solutions in the linear space generated by { sinh ( ω t ) , cosh ( ω t ) } , the estimate of the local error behaves as O ( h 4 ) and the high-order formula has fourth-order accuracy when the stepsize h → 0 . These new pairs are compared with another one proposed by Franco [J.M. Franco, An embedded pair of exponentially fitted explicit Runge–Kutta methods, J. Comput. Appl. Math. 149 (2002) 407–414] on several problems to test the efficiency of the new methods.

Stein's Method and Stochastic Analysis of Rademacher Functionals

We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein's method, as well as the use of appropriate discrete Malliavin operators. As the bounds are given in terms of Malliavin operators, no coupling construction is required. When the functional depends only on the first d coordinates of the Rademacher sequence, a simple sufficient condition for convergence to a normal distribution is derived. For finite quadratic forms, we obtain necessary and sufficient conditions. Although our approach does not require the classical use of exchangeable pairs, when the functional depends only on the first d coordinates of the Rademacher sequence we employ chaos expansion in order to construct an explicit exchangeable pair vector; the elements of the vector relate to the summands in the chaos decomposition and satisfy a linearity condition for the conditional expectation. Among several examples, such as random variables which depend on infinitely many Rademacher variables, we provide three main applications: (i) to CLTs for multilinear forms belonging to a fixed chaos, (ii) to the Gaussian approximation of weighted infinite 2-runs, and (iii) to the computation of explicit bounds in CLTs for multiple integrals over sparse sets. This last application provides an alternate proof (and several refinements) of a recent result by Blei and Janson.

Effect of Ionic Liquids on the Menschutkin Reaction: An Experimental and Theoretical Study

The effect of ionic liquids (ILs) on the Menschutkin reaction between N-methylimidazole and benzyl halides has been investigated. Hammett correlations have been used to obtain information on the reaction mechanism of benzyl chlorides in ionic and molecular solvents. The solvent effects on this reaction have been examined using both multiparameter linear solvation energy relationships and theoretical calculations. These latter have been performed using a supermolecular approach, i.e., the IL is represented by an explicit ionic pair, IP. Two possible different reaction pathways have been obtained changing the position of the IL-IP with respect to the reagents. It is hypothesized that inside the IL the Menschutkin reaction of benzyl chloride with N-methylimidazole can follow different reaction pathways by considering the influence of dynamic heterogeneity in ionic media on the time scale of the lifetime of a transition state.

Response disinhibition evoked by the administration of nicotine and nicotine-associated contextual cues

Nicotine causes dose-dependent alterations in accuracy on the differential-reinforcement of low-rate responding (DRL) 29.5-s schedule in rats. The current investigation evaluated whether nicotine-associated contextual cues can produce nicotine-like perturbations in DRL-schedule performance in the absence of nicotine. Nicotine and saline administrations occurred just prior to DRL 29.5-s schedule responding for sucrose solution, and two different experimental contexts (differentiated by visual, olfactory, and tactile cues) were utilized. All subjects ( N = 16) experienced two consecutive sessions of DRL-schedule responding per day. The experimental group ( n = 8) was exposed to saline immediately prior to the first session and 0.3 mg/kg nicotine before the second session, and the context was changed between sessions. This sequence of saline and then nicotine administration, paired with two reliable contexts, persisted for 12 consecutive days and successive nicotine administrations corresponded with increasingly poorer performance on the DRL 29.5-s schedule. No nicotine was administered for days 13-20 during context testing, and the nicotine-associated context produced response disinhibition on the DRL schedule. Two control groups were included in the design; subjects in one control group ( n = 4) received saline in each context to verify that the contexts themselves were not exerting control over operant responding. To assess how explicit and non-explicit pairings of nicotine and contextual cues influenced DRL behavior, subjects in a second control group ( n = 4) were given nicotine prior to the second session, but the contexts were not altered between sessions. The results from this experiment suggest that environmental stimuli associated with nicotine exposure can come to elicit nicotine-induced performance decrements on a DRL 29.5-s schedule.