Non-trivial Combination Research Articles

A Local Epsilon Version of Reed's Conjecture

In 1998, Reed conjectured that every graph of maximum degree Δ and clique number ω can be colored with ⌈12(Δ+1+ω)⌉ colors, significantly strengthening Brooks' Theorem. As evidence for his conjecture, he proved that this is true instead when the number of colors is some nontrivial convex combination of Δ+1 and ω. I 1979, Erdős, Rubin, and Taylor proved that a connected graph G is L-colorable for every list-assignment L satisfying |L(v)|≥d(v) for all v∈V(G), unless every block of G is a clique or odd cycle. We ask if every graph G is L-colorable for every list-assignment L satisfying |L(v)|≥⌈12(d(v)+1+ω(v))⌉, where ω(v) denotes the size of the largest clique in G containing v. We prove that this is true instead when |L(v)| is some nontrivial convex combination of d(v)+1 and ω(v), under certain mild assumptions.

On the List Coloring Version of Reed's Conjecture

The chromatic number of a graph is bounded below by its clique number and from above by its maximum degree plus one. In 1998, Reed conjectured that the chromatic number is at most halfway in between these trivial lower and upper bounds. Moreover, Reed proved that its at most some non-trivial convex combination of the two bounds. In 2012, King and Reed produced a short proof that, provided the maximum degree is large enough, a combination of 1/130,000 suffices. Recently Bonamy, Perrett, and the second author improved this to 1/26.It is natural to wonder if similar results hold for the list chromatic number. Unfortunately, previous techniques for ordinary coloring do not extend to list coloring. In this paper, we overcome these hurdles by introducing several new ideas. Our main result is that the list chromatic number is at most some non-trivial convex combination of the clique number and the maximum degree plus one. Furthermore, we show that for large enough maximum degree, that a combination of 1/13 suffices. Note that this also improves on the best known results for ordinary coloring.

4d mathcal{N} =2 theories with disconnected gauge groups

In this paper we present a beautifully consistent web of evidence for the existence of interacting 4d rank-1 mathcal{N} = 2 SCFTs obtained from gauging discrete subgroups of global symmetries of other existing 4d rank-1 mathcal{N} = 2 SCFTs. The global symmetries that can be gauged involve a non-trivial combination of discrete subgroups of the U(1)R, low-energy EM duality group mathrm{S}mathrm{L}left(2,kern0.5em mathbb{Z}right) , and the outer automorphism group of the flavor symmetry algebra, Out(F ).The theories that we construct are remarkable in many ways: (i) two of them have exceptional F4 and G2 flavor groups; (ii) they substantially complete the picture of the landscape of rank-1 mathcal{N} = 2 SCFTs as they realize all but one of the remaining consistent rank-1 Seiberg-Witten geometries that we previously constructed but were not associated to known SCFTs; and (iii) some of them have enlarged mathcal{N} = 3 SUSY, and have not been previously constructed. They are also examples of SCFTs which violate the ShapereTachikawa relation between the conformal central charges and the scaling dimension of the Coulomb branch vev. We propose a modification of the formulas computing these central charges from the topologically twisted Coulomb branch partition function which correctly compute them for discretely gauged theories.

Using Scheffé projections for multiple outcomes in an observational study of smoking and periodontal disease

In an observational study of the effects caused by treatments, a sensitivity analysis asks about the magnitude of bias from unmeasured covariates that would need to be present to alter the conclusions of a naive analysis that presumes adjustments for measured covariates remove all biases. When there are two or more outcomes in an observational study, these outcomes may be unequally sensitive to unmeasured biases, and the least sensitive finding may concern a combination of several outcomes. A method of sensitivity analysis is proposed using Scheffé projections that permits the investigator to consider all linear contrasts in two or more scored outcomes while controlling the family-wise error rate. In sufficiently large samples, the method will exhibit insensitivity to bias that is greater than or equal to methods, such as the Bonferroni–Holm procedure, that focus on individual outcomes; that is, Scheffé projections have larger design sensitivities. More precisely, if the least sensitive linear combination is a single one of the several outcomes, then the design sensitivity using Scheffé projections equals that using a Bonferroni correction, but if the least sensitive combination is a nontrivial combination of two or more outcomes, then Scheffé projections have larger design sensitivities. This asymptotic property is examined in terms of finite sample power of sensitivity analyses using simulation. The method is applied to a replication with recent data of a well-known study of the effects of smoking on periodontal disease. In the example, the comparison that is least sensitive to bias from unmeasured covariates combines results for lower and upper teeth, but emphasizes lower teeth. This pattern would be difficult to anticipate prior to examining the data, but Scheffé’s method permits use of this unanticipated pattern without fear of capitalizing on chance.

Effect of graphene support on large Pt nanoparticles.

State-of-the-art catalysts are often created via deposition of monolayers, sub-monolayers or nanoparticles of the catalytic material over supports, aiming to increase the surface area and decrease the loading of the catalytic material and therefore the overall cost. Here, we employ large-scale DFT calculations to simulate platinum clusters with up to 309 atoms interacting with single layer graphene supports with up to 880 carbon atoms. We compute the adsorption, cohesion and formation energies of two and three-dimensional Pt clusters interacting with the support, including dispersion interactions via a semi-empirical dispersion correction and a vdW functional. We find that three-dimensional Pt clusters are more stable than the two-dimensional when interacting with the support, and that the difference between their stabilities increases with the system size. Also, the dispersion interactions are more pronounced as we increase the nanoparticle size, being essential to a reliable description of larger systems. We observe inter-atomic expansion (contraction) on the closest (farthest) Pt facets from the graphene sheet and charge redistribution with overall charge being transferred from the platinum clusters to the support. The Pt-Pt expansion, which is related to the charge transfer in the system, correlates with the adsorption energy per Pt atom in contact with the graphene. These, and other electronic and structural observations show that the effect of the support cannot be neglected. Our study provides for the first time, to the best of our knowledge, quantitative results on the non-trivial combination of size and support effects for nanoparticles sizes which are relevant to catalyst design.

A novel generator for high-voltage bipolar square pulses with applications in sterilization of microorganism

In this paper, we propose and design a novel generator for the high voltage square pulses with the changeable polarities in order to reach the requirements and the needs for the intended experiments on sterilization of microorganism. The major component of our circuits is a non-trivial combination between a half bridge Marx generator and an H bridge in series, combining with the DSP control unit, which can adjust the voltages, frequencies, pulse widths and polarities, and also tolerate various loads. More precisely, we illustrate the design and operation principles for each module in the constructed circuit and analyze the system performance with various loads. The effectiveness and correctness of our proposed circuit and methodologies have been verified and demonstrated by both PSIM simulation results and our own prototype. In this paper, we also show the stability and reliability of the pulse generator we proposed in terms of various load conditions and operation safety respectively. Furthermore, we also observe that the key parameters based on our constructed pulse generator can be easily adjusted which include voltages, frequencies, pulse widths and polarities. We hope that our work will stimulate the further investigations on design and analysis of pulse generators with a focus on modularization and miniaturization.

Dependence Measuring from Conditional Variances

Abstract A conditional variance is an indicator of the level of independence between two random variables. We exploit this intuitive relationship and define a measure v which is almost a measure of mutual complete dependence. Unsurprisingly, the measure attains its minimum value for many pairs of non-independent ran- dom variables. Adjusting the measure so as to make it invariant under all Borel measurable injective trans- formations, we obtain a copula-based measure of dependence v* satisfying A. Rényi’s postulates. Finally, we observe that every nontrivial convex combination of v and v* is a measure of mutual complete dependence.

On guided versus deflected fields in controlled-source electromagnetics

Abstract The detection of electrically resistive targets in applied geophysics is of interest to the hydrocarbon, mining and geotechnical industries. Elongated thin resistive bodies have been extensively studied in the context of offshore hydrocarbon exploration. Such targets guide electromagnetic fields in a process which superficially resembles seismic refraction. On the other hand, compact resistive bodies deflect current in a process which has more similarities to diffraction and scattering. The response of a real geological structure is a non-trivial combination of these elements—guiding along the target and deflection around its edges. In this note the electromagnetic responses of two end-member models are compared: a resistive layer, which guides the electromagnetic signal, and a resistive cylinder, which deflects the fields. Results show that the response of a finite resistive target tends to saturate at a much lower resistivity than a resistive layer, under identical survey configurations. Furthermore, while the guided electromagnetic fields generated by a buried resistive layer contain both anomalous horizontal and vertical components, the process of electromagnetic deflection from a buried resistive cylinder creates mainly anomalous vertical fields. Finally, the transmitter orientation with respect to the position of a finite body is an important survey parameter: when the distance to the target is much less than the host skin depth, a transmitter pointing towards the resistive cylinder will produce a stronger signal than a transmitter oriented azimuthally with respect to the cylinder surface. The opposite situation is observed when the distance to the target is greater than the host skin depth.

Experimental construction of generic three-qubit states and their reconstruction from two-party reduced states on an NMR quantum information processor

We experimentally explore the state space of three qubits on a nuclear magnetic resonance (NMR) quantum-information processor. We construct a scheme to experimentally realize a canonical form for general three-qubit states up to single-qubit unitaries. This form involves a nontrivial combination of Greenberger-Horne-Zeilinger (GHZ) and $W$-type maximally entangled states of three qubits. The general circuit that we have constructed for the generic state reduces to those for GHZ and $W$ states as special cases. The experimental construction of a generic state is carried out for a nontrivial set of parameters and the good fidelity of preparation is confirmed by complete state tomography. The GHZ and $W$ states are constructed as special cases of the general experimental scheme. Further, we experimentally demonstrate a curious fact about three-qubit states, where for almost all pure states, the two-qubit reduced states can be used to reconstruct the full three-qubit state. For the case of a generic state and for the $W$ state, we demonstrate this method of reconstruction by comparing it to the directly tomographed three-qubit state.

A branch-price-and-cut algorithm for the minimum evolution problem

We investigate the Minimum Evolution Problem (MEP), an NP-hard network design problem arising from computational biology. The MEP consists in finding a weighted unrooted binary tree having n leaves, minimal length, and such that the sum of the edge weights belonging to the unique path between each pair of leaves is greater than or equal to a prescribed value. We study the polyhedral combinatorics of the MEP and investigate its relationships with the Balanced Minimum Evolution Problem. We develop an exact solution approach for the MEP based on a nontrivial combination of a parallel branch-price-and-cut scheme and a non-isomorphic enumeration of all possible solutions to the problem. Computational experiments show that the new solution approach outperforms the best mixed integer linear programming formulation for the MEP currently described in the literature. Our results give a perspective on the combinatorics of the MEP and suggest new directions for the development of future exact solution approaches that may turn out useful in practical applications. We also show that the MEP is statistically consistent.

Interaction of Phase Transformations and Plasticity at the Nanoscale: Phase Field Approach

Phase field approach (PFA) to the interaction between phase transformations (PTs) and dislocations is developed at large strains as a nontrivial combination of our recent advanced PFAs to martensitic PTs and dislocation evolution. Finite element method (FEM) simulations are performed to solve the coupled phase-field and elasticity equations and are applied to study of the growth and arrest of martensitic plate for temperature-induced PTs, the evolution of dislocations and high pressure phase in a nanograined material under pressure and shear, and the dislocation inheritance for stress-induced PT.

Transport equations for subdiffusion with nonlinear particle interaction.

We show how the nonlinear interaction effects 'volume filling' and 'adhesion' can be incorporated into the fractional subdiffusive transport of cells and individual organisms. To this end, we use microscopic random walk models with anomalous trapping and systematically derive generic non-Markovian and nonlinear governing equations for the mean concentrations of the subdiffusive cells or organisms. We uncover an interesting interaction between the nonlinearities and the non-Markovian nature of the transport. In the subdiffusive case, this interaction manifests itself in a nontrivial combination of nonlinear terms with fractional derivatives. In the long time limit, however, these equations simplify to a form without fractional operators. This provides an easy method for the study of aggregation phenomena. In particular, this enables us to show that volume filling can prevent "anomalous aggregation," which occurs in subdiffusive systems with a spatially varying anomalous exponent.

Jump in fluid properties of inflationary universe to reconcile scalar and tensor spectra

The recent detection of the B-mode polarization from the BICEP2 observation, if confirmed to be primordial, seems to be in tension with the upper bound on the amplitude of tensor perturbations from the PLANCK data. We consider a phenomenological model of inflation in which the microscopical properties of the inflationary fluid such as the equation of state $w$ or the sound speed ${c}_{s}$ jump in a sharp manner. We show that the amplitude of the scalar perturbations is controlled by a nontrivial combination of $w$ and ${c}_{s}$ before and after the phase transition while the tensor perturbations remains nearly intact. With an appropriate choice of the fluid parameters $w$ and ${c}_{s}$ one can suppress the scalar perturbation power spectrum on large scales to accommodate a large tensor amplitude.

A modelling framework for the olfactory system of the honeybee using GeNN (GPU enhanced Neuronal Network simulation environment)

We present an example implementation of a minimalmodel of honeybee olfactory system on massively paral-lel GPU hardware using GPU-specific code generationwith GeNN[1]. This will be a first step to provide a phy-siologically coherent model of the honeybee olfactorysystem to be implemented in real time on fying autono-mous robots for the “Green Brain Project”.The “Green Brain Project” will combine computationalneuroscience modelling, learning and decision theory,modern parallel computing methods and robotics withdata from state-of-the-art neurobiological experimentson cognition in the honeybee Apis mellifera, to buildand deploy a modular model of the honeybee braindescribing detection, classification and learning in theolfactory and optic pathwaysaswellasmulti-sensoryintegration across these sensory modalities. Unlike otherbrain models, which use expensive traditional supercom-puting resources,the ‘Green Brain’ will be implementedon massively parallel, but affordable GPU technology.The ‘Green Brain’ will be deployed for the real-timecontrol of a flying robot able to sense and act autono-mously. This robot testbed will be used to demonstratethe development of new biomimetic control algorithmsfor artificial intelligence and robotics applications.The objective for modelling olfaction in the“GreenBrain Project” will extend previous attempts to model theantennal lobes and their constituent glomeruli (whichencode olfactory cues), the projection neurons and themushroom bodies. Odours are known to have a distribu-ted representation in the antennal lobe, encoded as differ-ential activation levels of glomerular populations. Odourmixtures are represented as a non-trivial combination ofconstituent odours’ representations, and formation oflong-term memories associated with such odour mixtureshas been shown to induce volume changes in glomeruliindicating a cross-inhibitory effect between neural codings[2]. The modelling will also consider how mechanismsmight implement known classification rules, such as in themodels of insect olfactory classification by Huerta et al. [3]and Nowotny et al. [4].In this study, we present some benchmarking results.We perform performance and scalability tests on an NVI-DIA Tesla C2070 GPU with an Intel

Inside and outside stories of black-branes in anti de Sitter space

In this paper, we investigate the dynamics inside and outside of black-branes in anti de Sitter space by numerical simulations using double-null formalism. We prepare a charged planar matter shell which, due to a negative cosmological constant, collapses and dynamically forms a black-brane with an apparent horizon, a singularity and a Cauchy horizon. The gravitational collapse cannot form a naked overcharged black-brane and hence weak cosmic censorship is safe. Although mass inflation occurs, the effect is much milder than in the case of charged black holes; hence, strong cosmic censorship seems not to be safe. We observed the scalar field dynamics outside the horizon. There should remain a non-trivial scalar field combination—‘charge cloud’—between the horizon and the boundary. This can give some meaning in terms of the AdS/CFT correspondence.

Toeplitz operators on the pluriharmonic Hardy space

Corresponding to harmonic Bergman space, in this paper we study Toeplitz operators of pluriharmonic Hardy space. We find the properties of Toeplitz operators on h 2 ( D 2 ) are greatly different from the classical Hardy space, Bergman space and harmonic Bergman space. For example, two analytic Toeplitz operators maybe not semi-commute or commute. Even if it is semi-commute, neither of both symbols is constant; Even if it is commute, their symbols’ nontrivial linear combination may be not constant. We obtain the necessary and sufficient condition of two analytic Toeplitz operators semi-commute and commute on h 2 ( D 2 ).

Microbial effects on the release and attenuation of arsenic in the shallow subsurface of a natural geochemical anomaly

Critical factors leading to arsenic release and attenuation from the shallow subsurface were studied with multidisciplinary approach in the natural gold–arsenic geochemical anomaly at Mokrsko (Czech Republic). The results show that microbial reduction promotes arsenic release from Fe(III) (hydr)oxides and Fe(III) arsenates, thereby enhancing dissolved arsenic in the shallow groundwater at average concentration of 7.76 mg/L. In the organic-rich aggregates and wood particles, however, microbial sulfate reduction triggers the formation of realgar deposits, leading to accumulation of As in the distinct organic-rich patches of the shallow subsurface. We conclude that precipitation of realgar in the shallow subsurface of soil/sediment depends on specific and non-trivial combination of water and rock chemistry, microbial community composition and spatial organisation of the subsurface zone, where speciation in saturated environments varied on a centimeter scale from reduced (decomposed wood, H2S and realgar present) to oxidized (goethite and arsenate minerals are present).

РЕПУТАЦИЯ ЮРГИСА БАЛТРУШАЙТИСА В БАЛТИЙСКОЙ РУССКОЙ ПЕЧАТИ 1920–1930-Х ГОДОВ

This paper analyzes the reputation of Jurgis Baltrušaitis in the interwar Baltic Russian periodic press (Echo, Ponedelnik in Kaunas, Segodnya, Dlia Vas in Riga, and others). Its primary component was the of the Lithuanian diplomatic representative in Russia the activity of the, which in many ways was reflected in Russian newspapers’ messages, articles, and feuilletons. The diplomatic activity actualized Baltrušaitis as a poet and translator, and his creative work met some newspapers’ program provisions to promote Lithuanian culture. However, modest in scale and results, his actual work had little impact on the poet’s and diplomat’s literary reputation. The latter was formed by the earlier Russian poet’s and translator’s, one of the Russian symbolism creator’s merits. The nontrivial combination of a poet’s and a diplomat’s roles, an unusual situation at the Lithuanian and Russian cultural crossroads, the paradox of a Russian poet of Lithuanian origin was of special relevance for the national state building and a new political, civic, and ethnic identity formation era.

Wronskians and deep zeros of holomorphic functions

Given linearly independent holomorphic functions f0,…,fn on a planar domain Ω, let E be the set of those points z∈Ω where a nontrivial linear combination ∑j=0nλjfj may have a zero of multiplicity greater than n, once the coefficients λj=λj(z) are chosen appropriately. An elementary argument involving the Wronskian W of the fjʼs shows that E is a discrete subset of Ω (and is actually the zero set of W); thus “deep” zeros are rare. We elaborate on this by studying similar phenomena in various function spaces on the unit disk, with more sophisticated boundary smallness conditions playing the role of deep zeros.

MRI: Modular reasoning about interference in incremental programming

AbstractIncremental Programming(IP) is a programming style in which new program components are defined as increments of other components. Examples of IP mechanisms includeObject-oriented programminginheritance,aspect-oriented programmingadvice, andfeature-oriented programming. A characteristic of IP mechanisms is that, while individual components can be independently defined, the composition of components makes those components become tightly coupled, sharing both control and data flows. This makes reasoning about IP mechanisms a notoriously hard problem:modular reasoningabout a component becomes very difficult; and it is very hard to tell if two tightly coupled componentsinterferewith each other's control and data flows. This paper presentsmodular reasoning about interference(MRI), apurely functionalmodel of IP embedded in Haskell. MRI models inheritance with mixins and side effects with monads. It comes with a range of powerful reasoning techniques: equational reasoning, parametricity, and reasoning with algebraic laws about effectful operations. These techniques enable MRI in the presence of side effects. MRI formally capturesharmlessness, a hard-to-formalize notion in the interference literature, in two theorems. We prove these theorems with a non-trivial combination of all three reasoning techniques.