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The structural variations of multidomain proteins with flexible parts mediate many biological processes, and a structure ensemble can be determined by selecting a weighted combination of representative structures from a simulated structure pool, producing the best fit to experimental constraints such as interatomic distance. In this study, a hybrid structure-based and physics-based atomistic force field with an efficient sampling strategy is adopted to simulate a model di-domain protein against experimental paramagnetic relaxation enhancement (PRE) data that correspond to distance constraints. The molecular dynamics simulations produce a wide range of conformations depicted on a protein energy landscape. Subsequently, a conformational ensemble recovered with low-energy structures and the minimum-size restraint is identified in good agreement with experimental PRE rates, and the result is also supported by chemical shift perturbations and small-angle X-ray scattering data. It is illustrated that the regularizations of energy and ensemble-size prevent an arbitrary interpretation of protein conformations. Moreover, energy is found to serve as a critical control to refine the structure pool and prevent data overfitting, because the absence of energy regularization exposes ensemble construction to the noise from high-energy structures and causes a more ambiguous representation of protein conformations. Finally, we perform structure-ensemble optimizations with a topology-based structure pool, to enhance the understanding on the ensemble results from different sources of pool candidates.

We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places N identical point charges at a closed curve T at the same arc-length distances and asks about the energy minimum, ie which shape does the loop take if left by itself. The second problem comes from quantum mechanics: we take a Schrdinger operator in

The concept of matrix canonical realization of a Lie algebra is introduced. The generators of the Lie algebra of the pseudoorthogonal group n) are recurrently expressed in terms of matrices with polyno-mial elements in a certain number of quantum-mechanical canonical variables p~, qi and they depend on a certain number of free real para-meters. The realizations are, in the well-defined sense, skew-hermitean and Casimir operators are multiples of the identity element. Part of them are usual canonical realizations.

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We propose a new basic trapdoor ℓIC (ℓ-Invertible Cycles) of the mixed field type for Multivariate Quadratic public key cryptosystems. This is the first new basic trapdoor since the invention of Unbalanced Oil and Vinegar in 1997. ℓIC can be considered an extended form of the well-known Matsumoto-Imai Scheme A (also MIA or C^∗), and share some features of stagewise triangular systems. However ℓIC has very distinctive properties of its own. In practice, ℓIC is much faster than MIA, and can even match the speed of single-field MQ schemes.

The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a potential and a vector potential coupled to the loose edges by a coupling. It is shown that if the lengths of the connecting edges shrink to zero and the potentials are properly scaled, the limit can yield any prescribed singular vertex coupling, and moreover, that such an approximation converges in the norm-resolvent sense.

Representations of the sl (n+ 1, C) Lie algebras are constructed with the help of canonical (boson) realisations of these algebras. For every weight Lambda on the standard Cartan subalgebra of sl (n+ 1, C) the authors obtain a representation rho Lambda (n+ 1)(called the maximal representation) which contains an irreducible subrepresentation with Lambda as the highest weight. It is shown that for a major part of the weights Lambda the representations rho Lambda (n+ 1) themselves are irreducible. The standard construction of the highest-weight representations of semi-simple Lie algebras is based on the so-called elementary representations; comparing with them, the authors maximal representations are given in the explicit form.

Feature distillation, a primary method in knowledge distillation, always leads to significant accuracy improvements. Most existing methods distill features in the teacher network through a manually designed transformation. In this paper, we propose a novel distillation method named task-oriented feature distillation (TOFD) where the transformation is convolutional layers that are trained in a data-driven manner by task loss. As a result, the task-oriented information in the features can be captured and distilled to students. Moreover, an orthogonal loss is applied to the feature resizing layer in TOFD to improve the performance of knowledge distillation. Experiments show that TOFD outperforms other distillation methods by a large margin on both image classification and 3D classification tasks. Codes have been released in Github[3].

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We study singular Schrdinger operators with an attractive interaction supported by a closed smooth surface AR3 and analyze their behavior in the vicinity of the critical situation where such an operator has empty discrete spectrum and a threshold resonance. In particular, we show that if A is a sphere and the critical coupling is constant over it, any sufficiently small smooth area-preserving radial deformation gives rise to isolated eigenvalues. On the other hand, the discrete spectrum may be empty for general deformations. We also derive a related inequality for capacities associated with such surfaces.

In this note we prove that the essential spectrum of a Schrdinger operator with potential supported on a finite number of compact Lipschitz hypersurfaces is given by [0, +). We emphasize that the union of a family of Lipschitz hypersurfaces is in general not Lipschitz. ( 2013 WileyVCH Verlag GmbH & Co. KGaA, Weinheim)

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We consider resonant vortices around nodal points of the wave function describing electron transport through a mesoscopic device. With a suitable choice of the device geometry, the dominating role is played by single vortices with a preferred orientation. To characterize the strength of the resulting magnetic moment, we have introduced a magnetance, the quantity defined in analogy with the device conductance. Its basic properties and possible experimental detection are discussed.

At the age of almost three quarters of a century, quantum mechanics is by all accounts a mature theory. There were times when it seemed that it had borne its best fruit already and would give way to investigation of deeper levels of matter. Today this sounds like rash thinking. Modern experimental techniques have led to discoveries of numerous new quantum effects in solid state, optics and elsewhere. Quantum mechanics is thus gradually becoming a basis for many branches of applied physics, in this way entering our everyday life. While the dynamic laws of quantum mechanics are well known, a proper theoretical understanding requires methods which would allow us to de rive the abundance of observed quantum effects from the first principles. In many cases the rich structure hidden in the Schr6dinger equation can be revealed only using sophisticated tools. This constitutes a motivation to investigate rigorous methods which yield mathematically well-founded properties of quantum systems.

The HFEv- signature scheme is one of the most studied multivariate schemes and one of the major candidates for the upcoming standardization of post-quantum digital signature schemes. In this paper, we propose three new attack strategies against HFEv-, each of them using the idea of projection. Especially our third attack is very effective and is, for some parameter sets, the most efficient known attack against HFEv-. Furthermore, our attack requires much less memory than direct and rank attacks. By our work, we therefore give new insights in the security of the HFEv- signature scheme and restrictions for the parameter choice of a possible future standardized HFEv- instance.

We consider Schrdinger operators in L2(R3) with a singular interaction supported by a finite curve . We present a proper definition of the operators and study their properties, in particular, we show that the discrete spectrum can be empty if is short enough. If it is not the case, we investigate properties of the eigenvalues in the situation when the curve has a hiatus of length 2. We derive an asymptotic expansion with the leading term which a multiple of ln.

Collecting paired training data is difficult in practice, but the unpaired samples broadly exist. Current approaches aim at generating synthesized training data from the unpaired samples by exploring the relationship between the corrupted and clean data. This work proposes LUD-VAE, a deep generative method to learn the joint probability density function from data sampled from marginal distributions. Our approach is based on a carefully designed probabilistic graphical model in which the clean and corrupted data domains are conditionally independent. Using variational inference, we maximize the evidence lower bound (ELBO) to estimate the joint probability density function. Furthermore, we show that the ELBO is computable without paired samples under the inference invariant assumption. This property provides the mathematical rationale of our approach in the unpaired setting. Finally, we apply our method to real-world image denoising and super-resolution tasks and train the models using the synthetic data generated by the LUD-VAE. Experimental results validate the advantages of our method over other learnable approaches.

In this paper, we developed a feasible and efficient deep-learning-based framework to combine the United States (US) natality data for the last five decades, with changing variables and factors, into a consistent database. We constructed a graph based on the property and elements of databases, including variables, and conducted a graph convolutional network (GCN) to learn the embeddings of variables on the constructed graph, where the learned embeddings implied the similarity of variables. Specifically, we devised a loss function with a slack margin and a banlist mechanism (for a random walk) to learn the desired structure (two nodes sharing more information were more similar to each other.), and developed an active learning mechanism to conduct the harmonization. Toward a total of 9,321 variables from 49 databases (i.e., 783 stemmed variables, from 1970 to 2018), we applied our model iteratively together with human reviews for four rounds, then obtained 323 hyperchains of variables. During the harmonization, the first round of our model achieved recall and precision of 87.56%, 57.70%, respectively. Our harmonized graph neural network (HGNN) method provides a feasible and efficient way to connect relevant databases at a meta-level. Adapting to the database's property and characteristics, HGNN can learn patterns globally, which is powerful to discover the similarity between variables among databases. Our proposed method provides an effective way to reduce the manual effort in database harmonization and integration of fragmented data into useful databases for future research.

We study spectral and scattering properties of a spinless quantum particle confined to an infinite planar layer with hard walls containing a finite number of point perturbations. A solvable character of the model follows from the explicit form of the Hamiltonian resolvent obtained by means of Kreins formula. We prove the existence of bound states, demonstrate their properties, and find the on-shell scattering operator. Furthermore, we analyze the situation when the system is put into a homogeneous magnetic field perpendicular to the layer; in that case the point interactions generate eigenvalues of a finite multiplicity in the gaps of the free Hamiltonian essential spectrum.

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In this paper we obtain sharp LiebThirring inequalities for a Schrdinger operator on semiaxis with a matrix potential and show how they can be used to other related problems. Among them are spectral inequalities on star graphs and spectral inequalities for Schrdinger operators on half-spaces with Robin boundary conditions.

We investigate non-equilibrium particle transport in a system consisting of a geometric scatterer and two leads coupled to heat baths with different chemical potentials. We derive an expression for the corresponding current, the carriers of which are fermions, and analyze numerically its dependence on the model parameters in examples where the scatterer has a rectangular or triangular shape.