Exact State Research Articles

The cut operation in subclasses of convex languages

The cut of two languages is a subset of their concatenation given by the leftmost maximal prefix match. We study the state complexity of the cut operation assuming that both operands belong to some, possibly different, subclasses of convex languages, namely, right, left, two-sided, and all-sided ideal, prefix-, suffix-, factor-, and subword-closed, -free, and proper convex languages. This state complexity is defined as the function that assigns the maximal state complexity of the language resulting from the cut operation to the pair of numbers m and n representing the sizes of deterministic finite automata recognizing the operands of this operation. For all considered pairs of classes, we get the exact state complexity of cut. We show that it is m or 1 whenever the first language is a right ideal, and it is m+n−1 or m+n−2 if the first language is prefix-closed, prefix-free, or proper prefix-convex. In the other cases, the state complexity of cut is between mn−2n−m+4 and mn−n+m, the latter being the known state complexity of cut on regular languages. All our witnesses are described over a fixed alphabet of size at most three, except for four cases when the witness languages are described over an alphabet of size m or m−1.

Many-body correlations in one-dimensional optical lattices with alkaline-earth(-like) atoms

We explore the rich nature of correlations in the ground state of ultracold atoms trapped in state-dependent optical lattices. In particular, we consider interacting fermionic ytterbium or strontium atoms, realizing a two-orbital Hubbard model with two spin components. We analyze the model in one-dimensional setting with the experimentally relevant hierarchy of tunneling and interaction amplitudes by means of exact diagonalization and matrix product states approaches, and study the correlation functions in density, spin, and orbital sectors as functions of variable densities of atoms in the ground and metastable excited states. We show that in certain ranges of densities these atomic systems demonstrate strong density-wave, ferro- and antiferromagnetic, as well as antiferroorbital correlations.

Phase separation of intrinsically disordered FG-Nups is driven by highly dynamic FG motifs

The intrinsically disordered FG-Nups in the central channel of the nuclear pore complex (NPC) form a selective permeability barrier, allowing small molecules to traverse by passive diffusion, while large molecules can only translocate with the help of nuclear transport receptors. The exact phase state of the permeability barrier remains elusive. In vitro experiments have shown that some FG-Nups can undergo phase separation into condensates that display NPC-like permeability barrier properties. Here, we use molecular dynamics simulations at amino acid resolution to study the phase separation characteristics of each of the disordered FG-Nups of the yeast NPC. We find that GLFG-Nups undergo phase separation and reveal that the FG motifs act as highly dynamic hydrophobic stickers that are essential for the formation of FG-Nup condensates featuring droplet-spanning percolated networks. Additionally, we study phase separation in an FG-Nup mixture that resembles the NPC stoichiometry and observe that an NPC condensate is formed containing multiple GLFG-Nups. We find that the phase separation of this NPC condensate is also driven by FG-FG interactions, similar to the homotypic FG-Nup condensates. Based on the observed phase separation behavior, the different FG-Nups of the yeast NPC can be divided into two classes: The FG-Nups (mostly GLFG-type) located in the central channel of the NPC form a highly dynamic percolated network formed by many short-lived FG-FG interactions, while the peripheral FG-Nups (mostly FxFG-type) at the entry and exit of the NPC channel likely form an entropic brush.

Bridging quantum criticality via many-body scarring

Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals -- a type of weak ergodicity breaking known as `quantum many-body scarring' (QMBS). Recent work [Phys.Rev.B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: as the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model -- a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.

Information-theoretic and algorithmic aspects of parallel and distributed reconstruction from pooled data

In the pooled data problem the goal is to efficiently reconstruct a binary signal from additive measurements. Given a signal σ∈{0,1}n, we can query multiple entries at once and get the total number of non-zero entries in the query as a result. We assume that queries are time-consuming and therefore focus on the setting where all queries are executed in parallel. First, we propose and analyze a simple and efficient greedy reconstruction algorithm. Secondly, we derive a sharp information-theoretic threshold for the minimum number of queries required to reconstruct σ with high probability. Finally, we consider two noise models: In the noisy channel model, the result for each entry of the signal flips with a certain probability. In the noisy query model, each query result is subject to random Gaussian noise. We pin down the range of error probabilities and distributions for which our algorithm reconstructs the exact initial states with high probability. Our theoretical findings are complemented by simulations where we compare our simple algorithm with approximate message passing (AMP) that is conjectured to be optimal in a number of related problems.

Monitored recurrence of a one-parameter family of three-state quantum walks

Monitored recurrence of a one-parameter set of three-state quantum walks on a line is investigated. The calculations are considerably simplified by choosing a suitable basis of the coin space. We show that the Polya number (i.e. the site recurrence probability) depends on the coin parameter and the probability that the walker is initially in a particular coin state for which the walk returns to the origin with certainty. Finally, we present a brief investigation of the exact quantum state recurrence.

An integrated modelling approach for targeted degradation: insights on optimization, data requirements and PKPD predictions from semi- or fully-mechanistic models and exact steady state solutions

The value of an integrated mathematical modelling approach for protein degraders which combines the benefits of traditional turnover models and fully mechanistic models is presented. Firstly, we show how exact solutions of the mechanistic models of monovalent and bivalent degraders can provide insight on the role of each system parameter in driving the pharmacological response. We show how on/off binding rates and degradation rates are related to potency and maximal effect of monovalent degraders, and how such relationship can be used to suggest a compound optimization strategy. Even convoluted exact steady state solutions for bivalent degraders provide insight on the type of observations required to ensure the predictive capacity of a mechanistic approach. Specifically for PROTACs, the structure of the exact steady state solution suggests that the total remaining target at steady state, which is easily accessible experimentally, is insufficient to reconstruct the state of the whole system at equilibrium and observations on different species (such as binary/ternary complexes) are necessary. Secondly, global sensitivity analysis of fully mechanistic models for PROTACs suggests that both target and ligase baselines (actually, their ratio) are the major sources of variability in the response of non-cooperative systems, which speaks to the importance of characterizing their distribution in the target patient population. Finally, we propose a pragmatic modelling approach which incorporates the insights generated with fully mechanistic models into simpler turnover models to improve their predictive ability, hence enabling acceleration of drug discovery programs and increased probability of success in the clinic.

Validasi Teorema Geometri pada kasus Titik Berat Segitiga secara Induktif Menggunakan Komputasi Simbolik

Symbolic computing emphasizes the exact processing of data representations. The exact representative states that even though the output is small, the data generated using processing can produce larger mathematical expressions. To overcome this problem, a method needs to be used in representing data. This process is carried out to solve a physical problem in the case of the center of gravity on a triangle. Symbolic programming languages can convert rational numbers, so that this symbolic processing can be applied to inductively validate geometric theorems in the case of triangular center.

Studying memory processes at different levels with simultaneous depth and surface EEG recordings.

Investigating cognitive brain functions using non-invasive electrophysiology can be challenging due to the particularities of the task-related EEG activity, the depth of the activated brain areas, and the extent of the networks involved. Stereoelectroencephalographic (SEEG) investigations in patients with drug-resistant epilepsy offer an extraordinary opportunity to validate information derived from non-invasive recordings at macro-scales. The SEEG approach can provide brain activity with high spatial specificity during tasks that target specific cognitive processes (e.g., memory). Full validation is possible only when performing simultaneous scalp SEEG recordings, which allows recording signals in the exact same brain state. This is the approach we have taken in 12 subjects performing a visual memory task that requires the recognition of previously viewed objects. The intracranial signals on 965 contact pairs have been compared to 391 simultaneously recorded scalp signals at a regional and whole-brain level, using multivariate pattern analysis. The results show that the task conditions are best captured by intracranial sensors, despite the limited spatial coverage of SEEG electrodes, compared to the whole-brain non-invasive recordings. Applying beamformer source reconstruction or independent component analysis does not result in an improvement of the multivariate task decoding performance using surface sensor data. By analyzing a joint scalp and SEEG dataset, we investigated whether the two types of signals carry complementary information that might improve the machine-learning classifier performance. This joint analysis revealed that the results are driven by the modality exhibiting best individual performance, namely SEEG.

Excited states of zero seniority based on a pair condensate

We study the excited states of zero seniority for various like-particle systems interacting by pairing forces and by general two-body interactions. We consider two types of excitations, generated from a ground state described by a pair condensate. One type is obtained by breaking a pair from the ground state condensate and replacing it by "excited" collective pairs built on time-reversed single-particle orbits. The second type of zero seniority excited states is described by a condensate of identical excited pairs. The structure of these excited states is analysed for the picked fence model and for the valence neutrons of $^{108}$Sn. For a state-depending pairing interaction, the first type of excited states agree well with the J=0 states which are known in $^{108}$Sn. At the same time, these states can be also associated unambiguously with those exact states which are the closest in energy to the experimental levels. The states corresponding to the excited pair condensate appear at low energies, around the energy of the second excited state of the first type, and they do not have a simple correspondence with exact eigenstates. However, at a much higher excitation energy there is an exact state which is similar in structure to an EPC state. It is shown that this EPC state has the features of a giant pairing vibration.

Improved Elastic Image Pair Method for Finding Transition States.

The elastic image pair (EIP) method is a robust method for finding approximate transition states between two local minima. However, the original implementation of the method had some limitations. In this work, we present an improved EIP method, in which the moving procedure of the image pair and the convergence strategy are modified. In addition, this method is combined with the rational function optimization method to give exact transition states. Tests on a set of 45 different reactions show the reliability and efficiency in finding transition states.

Formations and dynamics of two-dimensional spinning asymmetric quantum droplets controlled by a PT-symmetric potential.

In this paper, vortex solitons are produced for a variety of 2D spinning quantum droplets (QDs) in a PT-symmetric potential, modeled by the amended Gross-Pitaevskii equation with Lee-Huang-Yang corrections. In particular, exact QD states are obtained under certain parameter constraints, providing a guide to finding the respective generic family. In a parameter region of the unbroken PT symmetry, different families of QDs originating from the linear modes are obtained in the form of multipolar and vortex droplets at low and high values of the norm, respectively, and their stability is investigated. In the spinning regime, QDs become asymmetric above a critical rotation frequency, most of them being stable. The effect of the PT-symmetric potential on the spinning and nonspinning QDs is explored by varying the strength of the gain-loss distribution. Generally, spinning QDs trapped in the PT-symmetric potential exhibit asymmetry due to the energy flow affected by the interplay of the gain-loss distribution and rotation. Finally, interactions between spinning or nonspinning QDs are explored, exhibiting elastic collisions under certain conditions.

Quantum many-body scars in bipartite Rydberg arrays originating from hidden projector embedding

We study the nature of the ergodicity-breaking "quantum many-body scar" states that appear in the PXP model describing constrained Rabi oscillations. For a {wide class of bipartite lattices} of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's close proximity to a generalized projector-embedding form, a structure common to many models hosting quantum many-body scars. We construct a non-Hermitian, but strictly local extension of the PXP model hosting exact quantum scars, and show how various Hermitian scar-stabilizing extensions from the literature can be naturally understood within this framework. The exact scar states are obtained analytically as large spin states of explicitly constructed pseudospins. The quasi-periodic motion ensuing from the N\'eel state is finally shown to be the projection onto the Rydberg-constrained subspace of the precession of the large pseudospin.

Analytical Solutions of the Molecular Kratzer-Feus potential by means of the Nikiforov-Uvarov Method

The analytical methods for solving Schrödinger equation are essential and effective tools with which we can investigate the spectroscopic properties, the electronic structure, and the energetic properties of the diatomic molecules (DMs). Accordingly, in this work, we used the Nikiforov-Uvarov (NU) method to solve the three-dimensional nonrelativistic Schrödinger equation with the molecular Kratzer-Feus (KF) potential and obtain the exact analytical bound state energy eigenvalues as well as their corresponding normalized eigenfunctions. The effective KF diatomic molecular potential well is investigated and represented graphically for several well-known DMs. The bound state energy levels are tabulated numerically for arbitrary values of the vibrational and rotational quantum numbers. The results obtained in this work are found to be in excellent agreement with the already-existing results in the literature.

Configuration interaction based nonequilibrium steady state impurity solver

We present a solver for correlated impurity problems out of equilibrium based on a combination of the so-called auxiliary master equation approach (AMEA) and the configuration interaction expansion. Within AMEA one maps the original impurity model onto an auxiliary open quantum system with a restricted number of bath sites which can be addressed by numerical many-body approaches such as Lanczos/Arnoldi exact diagonalization (ED) or matrix product states (MPS). While the mapping becomes exponentially more accurate with increasing number of bath sites, ED implementations are severely limited due to the fast increase of the Hilbert space dimension for open systems, and the MPS solver typically requires rather long runtimes. Here, we propose to adopt a configuration interaction approach augmented by active space extension to solve numerically the correlated auxiliary open quantum system. This allows access to a larger number of bath sites at lower computational costs than for plain ED. We benchmark the approach with numerical renormalization group results in equilibrium and with MPS out of equilibrium. In particular, we evaluate the current, the conductance, as well as the Kondo peak and its splitting as a function of increasing bias voltage below the Kondo temperature ${T}_{\text{K}}$. We obtain a rather accurate scaling of the conductance as a function of the bias voltage and temperature rescaled by ${T}_{\text{K}}$ for moderate to strong interactions in a wide range of parameters. The approach combines the fast runtime of ED with an accuracy close to the one achieved by MPS making it an attractive solver for nonequilibrium dynamical mean field theory.

Multi species asymmetric simple exclusion process with impurity activated flips

We obtain an exact matrix product steady state for a class of multi species asymmetric simple exclusion process with impurities, under periodic boundary condition. Alongside the usual hopping dynamics, an additional flip dynamics is activated only in the presence of impurities. Although the microscopic dynamics renders the system to be non-ergodic, exact analytical results for observables are obtained in steady states for a specific class of initial configurations. Interesting physical features including negative differential mobility and transition of correlations from negative to positive with changing vacancy density, have been observed. We discuss plausible connections of this exactly solvable model with multi lane asymmetric simple exclusion processes as well as enzymatic chemical reactions.

On the flavor/mass dichotomy for mixed neutrinos: a phenomenologically motivated analysis based on lepton charge conservation in neutron decay

Flavor/mass dichotomy for mixed fields is one of the most controversial issues in Quantum Field Theory. In this work, we approach the problem by considering the mixing of neutrinos and computing the transition amplitude of the paradigmatic neutron beta-decay n,rightarrow , p ,+,e^-,+,{bar{nu }}. Calculations are developed by utilizing the following different representations of neutrino states: (1) Pontecorvo states, (2) mass states and (3) exact QFT flavor states, which are defined as eigenstates of the flavor charge. As a guiding principle, we invoke the conservation of lepton charge in the interaction vertex, which is fundamentally inbuilt into the Standard Model at tree level. In the short-time limit, we show that the only fully consistent scenario is that based on QFT states, whereas the other two frameworks contradict the underlying theory. This result provides a crucial step toward understanding the rôle of neutrino mixing in weak decays and contributes to elucidate the flavor/mass controversy in QFT.

Study of Defect-Induced Chemical Modifications in Spinel Zinc-Ferrites Nanostructures by In-Depth XPS Investigation

Spinel zinc ferrite nanomaterials with exceptional physiochemical properties are potential candidates for various applications in the energy and environmental fields. Their properties can be tailored using several methods to widen their applications. The chemical combustion approach was followed to prepare the spinel zinc ferrite nanomaterials, which were then subjected to thermal treatment at a fixed temperature. Thermal heat treatment at a fixed temperature was used to evaluate the phase and morphological characteristics of the prepared spinel zinc−ferrite nanocomposites. Various techniques were employed to examine the samples, including X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), Raman spectroscopy, and X-ray photoelectron spectroscopy (XPS). XPS and X-ray−induced Auger electron spectroscopy were used to extensively examine the surface characteristics of the zinc−ferrite. To study the actual chemical states of the synthesized spinel zinc ferrite nanomaterials and the defects created during the thermal treatment, an extensive investigation of the kinetic energy of the X-ray−induced Zn L3M45M45 and Fe L3M45M45 was conducted. Finally, a detailed analysis of the Wagner plot using the modified Auger parameter was performed to verify the exact chemical states of Zn and Fe. Thus, the findings of the investigation show that XPS is a promising and powerful technique to study the composition and chemical states of spinel zinc ferrites, providing an understanding of changes in their properties for functional applications.

Siamese residual network for efficient visual tracking

The Siamese tracking framework has attracted much attention due to its scalability and efficiency in recent years. However, it is less effective in recognizing arbitrary targets with various variations, especially in complex scenarios with background distractors and illumination variations. To this end, we propose a Siamese Residual Network to formulate the characteristics of a specific given target for visual tracking, consisting of an identity branch and a residual branch. The identity branch consists of a generic offline-trained similarity-matching network, which distinguishes the target from the background at the class level. To complement the identity branch for handling complex scenarios and dramatic target appearance variations, we develop a residual branch learned from the samples of exact target states and online distractors under the guidance of the identity branch. These two branches representing arbitrary targets with both class-level and sample-level features achieve accurate target localizations under complicated scenarios. In addition, we propose an adaptive KL-based scheme for updating the residual branch effectively by avoiding overfitting to a long-retained target appearance. Extensive experimental results on OTB-2013, OTB-2015, VOT2016, VOT-2018, VOT-2019, Temple-Color-128, and LaSOT show that the proposed method performs against state-of-the-art trackers.

Exact solution and coherent states of an asymmetric oscillator with position-dependent mass

We revisit the problem of the deformed oscillator with position-dependent mass [da Costa et al., J. Math. Phys. 62, 092101 (2021)] in the classical and quantum formalisms by introducing the effect of the mass function in both kinetic and potential energies. The resulting Hamiltonian is mapped into a Morse oscillator by means of a point canonical transformation from the usual phase space (x, p) to a deformed one (xγ, Πγ). Similar to the Morse potential, the deformed oscillator presents bound trajectories in phase space corresponding to an anharmonic oscillatory motion in classical formalism and, therefore, bound states with a discrete spectrum in quantum formalism. On the other hand, open trajectories in phase space are associated with scattering states and continuous energy spectrum. Employing the factorization method, we investigate the properties of the coherent states, such as the time evolution and their uncertainties. A fast localization, classical and quantum, is reported for the coherent states due to the asymmetrical position-dependent mass. An oscillation of the time evolution of the uncertainty relationship is also observed, whose amplitude increases as the deformation increases.