Search Results (22)

We apply extended local hidden-gauge formalism to study meson–meson interactions with the quark constituents $cc\overline{c}\overline{c}$, $cc\overline{c}\overline{b}/\overline{c}\overline{c}cb$, $cc\overline{b}\overline{b}/\overline{c}\overline{c}bb$, $bb\overline{c}\overline{b}/\overline{b}\overline{b}cb$, and $bb\overline{b}\overline{b}$, in which the exchanged mesons are the fully heavy vector mesons $J/\psi$, $B_c^{*}$ and $\mathrm{{\rm Y}}$. We solve the coupled-channel Bethe–Salpeter equation to derive two poles in the $bb\overline{c}\overline{b}$ system and two poles in the $cc\overline{c}\overline{b}$ system. There are also four charge-conjugated poles in the $\overline{b}\overline{b}cb$ and $\overline{c}\overline{c}cb$ systems. In the $bb\overline{c}\overline{b}$ system, one pole corresponds to a sub-threshold bound state when the cutoff momentum is set to $\mathrm{\Lambda }>850 \mathrm{MeV}$. The other pole in this system corresponds to a sub-threshold bound state when $\mathrm{\Lambda }>1100 \mathrm{MeV}$. In the $cc\overline{c}\overline{b}$ system, the two poles correspond to sub-threshold bound states only when $\mathrm{\Lambda }>1550 \mathrm{MeV}$ and $\mathrm{\Lambda }>2650 \mathrm{MeV}$. This makes them difficult to identify as deeply bound hadronic molecules. We propose investigating the two poles of the $bb\overline{c}\overline{b}$ system in the ${\mu }^{+}{\mu }^{-}{B}_c^{-}$ channel at the LHC. Full article

A major threat to biodiversity is represented by Invasive Alien Species (IAS), particularly on freshwater ecosystems, which are already heavily altered by human activities. Two of the most pernicious IAS are the eastern and western mosquitofish, i.e., Gambusia holbrooki and G. affinis. These two poeciliids are morphologically very close to each other, and soon after their formal description, G. holbrooki was considered a subspecies of G. affinis. In the following years, several studies proved that these two entities belonged to two different species; nevertheless, it was only at the end of the 1990s that their separate taxonomic status was re-established. In the 1920s and 1930s, both G. holbrooki and G. affinis were asynchronously introduced from the United States into Europe and subsequently translocated globally as biocontrol agents of the malaria vector (i.e., the larvae of the Anopheles mosquitoes), with dramatic consequences for the inland water native fauna. However, due to taxonomic uncertainties and nomenclatural instability, for years, there were doubts about which Gambusia species had been introduced in different regions. The first available molecular studies confirmed the occurrence of G. holbrooki in Europe, but no evidence confirming the occurrence of G. affinis was found. Despite this, some records report the occurrence of western mosquitofish in Italy and Malta. Considering the negative effects that the mosquitofish has on the native biota, it is of paramount importance to know the precise biological diversity of the native and non-native species to better implement environmental management strategies to properly preserve the already-fragile waterbodies. Therefore, to check for the possible occurrence of G. affinis in Italy and Malta, we conducted extensive sampling in Sicily (Italy) and in the Maltese archipelago, aiming to verify the identity of Gambusia populations occurring in the study area. Based on sequences of the mitochondrial cytochrome b gene, we consistently observed the occurrence of only G. holbrooki in the investigated area, finding, almost exclusively, the most common haplotype known for the species in the whole invaded range (i.e., “HOL1”). Full article

This paper explores the fractal properties of token embedding spaces in GPT-2 language models by analyzing the stability of the correlation dimension, a measure of geometric complexity. Token embeddings represent words or subwords as vectors in a high-dimensional space. We hypothesize that the correlation dimension $D_2$ remains consistent across different vocabulary subsets, revealing fundamental structural characteristics of language representation in GPT-2. Our main objective is to quantify and analyze the stability of $D_2$ in these embedding subspaces, addressing the challenges posed by their high dimensionality. We introduce a new theorem formalizing this stability, stating that for any two sufficiently large random subsets $S_1,S_2\subset E$, the difference in their correlation dimensions is less than a small constant $\epsilon$. We validate this theorem using the Grassberger–Procaccia algorithm for estimating $D_2$, coupled with bootstrap sampling for statistical consistency. Our experiments on GPT-2 models of varying sizes demonstrate remarkable stability in $D_2$ across different subsets, with consistent mean values and small standard errors. We further investigate how the model size, embedding dimension, and network depth impact $D_2$. Our findings reveal distinct patterns of $D_2$ progression through the network layers, contributing to a deeper understanding of the geometric properties of language model representations and informing new approaches in natural language processing. Full article

The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For any class of user task, these moments are the functions of the node resources, task numerical characteristics, and the parameters of the current node state. These functions of the vector arguments can be treated as some surfaces in the multidimensional Euclidean spaces, so the proposed models are called the stochastic time complexity surfaces. The paper also presents a class of functions suitable for the description of both the mean and variance. They contain unknown parameters which should be estimated. The article includes the statement of the parameter identification problem given the statistical results of the node stress testing, recommendations concerning the test planning, and preprocessing of the raw experiment data. To illustrate the performance of the proposed model, the authors design it for an actual database application—the prototype of the passengers’ personal data anonymization system. Its application functions are classified into two user task classes: the data anonymization procedures and fulfillment of the statistical queries. The authors identify the stochastic time complexity surfaces for both task types. The additional testing experiments confirm the high performance of the suggested model and its applicability to the solution of the practical providers’ problems. Full article

We propose analytical approximations of the reflection and transmission spectra of a stacked dielectric diffraction grating consisting of two identical resonant guided-mode gratings with a Lorentzian line shape. These approximations, derived using the scattering matrix formalism, are functions of both angular frequency $\omega$ and the tangential wave vector component $k_x$ of the incident wave. We analytically demonstrate and, using full-wave simulations with rigorous coupled-wave analysis technique, numerically confirm that by a proper choice of the thickness of the dielectric layer separating the gratings, one can tailor the resonant optical properties of the stacked structure. In particular, it is possible to obtain lines of quasi-bound states in the continuum in the $\omega –k_x$ parameter space with the quality factor decaying proportionally to $k_x^{-4}$ or $k_x^{-6}$. In addition, the stacked structure can be used as a spectral or spatial Butterworth filter operating in reflection. The presented results may find application in the design of optical filters and sensors based on stacked resonant gratings. Full article

A new route to the Dirac equation and its symmetries is outlined on the basis of the four-vector representation of the Lorentz group (LG). This way permits one to linearize the first Casimir operator of the LG in terms of the energy–momentum four-vector and enables one to derive an extended Dirac equation that naturally reveals the $SU\left(2\right)$ symmetry in connection with an isospin associated with the LG. The procedure gives a spin-one-half fermion doublet, which we interpret as the electron and neutrino or the up-and-down quark doublet. Similarly, the second Casimir operator can be linearized by invoking an abstract isospin that is not connected with the LG, but with the two basic empirical fermion types. Application of the spinor helicity formalism yields two independent singlet and triplet fermion states—which we interpret as being related to $U\left(1\right)$ and the lepton, respectively—to the $SU\left(3\right)$ symmetry group of the three colors of the quarks. The way in which we obtain these results indicates the genuine yet very different physical natures of these basic symmetries. This new notion does not need the idea of grand unification. However, by still combining them in the product group $SU\left(4\right)=SU\left(3\right)\otimes U\left(1\right)$ and then further combining all groups into $SU\left(2\right)\otimes SU\left(4\right)$, one may get a symmetry scheme that perhaps supports the notion of unification by the group $SU\left(8\right)$. We also argue that the simpler $SO\left(4\right)$ group—instead of $SU\left(4\right)$—seems more appropriate for achieving unification. Full article

Glaciation has been a powerful determiner of species distributions and the genetic structure of populations. Contemporary distributions of many organisms in North America’s Western Cordillera reflect the influence of Pleistocene glaciation. We identified a pattern of north–south differentiation in the genus Prosimulium of western North America, which reflects the separation of northern and southern populations by the North American Ice Sheet during the Pleistocene Epoch. The taxonomic implication is that new species exist within nominal species, requiring formal description or revalidation of names currently in synonymy. We morphologically and cytogenetically examined populations of one nominal species of black fly, Prosimulium esselbaughi Sommerman, over its known range from Alaska south to California and Colorado. Chromosomal and morphological evidence supports the presence of two species, P. esselbaughi sensu stricto from Alaska to at least southern British Columbia, and a new species, Prosimulium supernum in the central Rocky Mountains and high Sierra Nevada range of the United States. The new species is described in all life stages above the egg, along with its polytene chromosomes. The existence of differentiated populations of other nominal species of black flies in northern and southern North America provides a system for investigating possible co-differentiation of vectors and parasites. Full article

Capybaras (Hydrochoerus hydrochaeris) are the largest rodents on Earth. While capybaras are hosts for various tick species, there is limited information regarding the tick-borne pathogens they can carry. We investigated the presence of piroplasmids and Ehrlichia spp. in capybaras and their associated ticks in two peri-urban areas in Goiás state, central-western Brazil. Blood samples collected from 23 capybaras were used to investigate the presence of piroplasmids and Ehrlichia spp. in stained-blood smears and by PCR. Ticks collected from the capybaras were identified morphologically and also tested using PCR for the same pathogens. A total of 955 ticks were collected, including 822 (86.1%) Amblyomma sculptum, 132 (13.8%) Amblyomma dubitatum, and one (0.1%) unidentified larva of Amblyomma sp. Neither the capybaras nor ticks were positive for Ehrlichia spp. However, a stained-blood smear examination revealed the presence of ring-stage and pyriform-shaped merozoites in the erythrocytes of one (4.4%) capybara. In the same way, 47.8% (11/23) and 19.9% (36/181) of blood samples and ticks, respectively, were positive for piroplasmids in the PCR. We successfully sequenced a partial 18S rRNA gene fragment of four samples (two capybaras, one A. sculptum, and one A. dubitatum), and the phylogenetic reconstruction disclosed that the organism reported in the present study clusters within the genus Babesia. Further research is required for a formal delineation of this species (designated as Babesia sp. strain Capybara) and to investigate the hypothesis of A. dubitatum and A. sculptum ticks being vectors. Full article

Clarifying the nature of the quantum state $|\mathsf{\Psi }⟩$ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the ℂ-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice. Full article

The concepts of Weak Values (WV) and Two-State Vector Formalism (TSVF) appear to motivate new experiments and to offer novel insights into dynamical processes in various materials of several scientific and technological fields. To support this view, here we consider the dynamics of hydrogen atoms and/or molecules in nanostructured materials like e.g., carbon nanotubes. The experimental method applied is incoherent scattering of thermal (i.e., non-relativistic) neutrons (INS). In short, the main finding consists in the following effect: the measured energy and momentum transfers are shown to contradict even qualitatively the associated expectations of conventional scattering theory. This effect was recently observed in INS experiments, e.g., in H${}_2$ adsorbed in carbon nanotubes, where a large momentum transfer deficit was found. Due to the broad abundance of hydrogen, these findings may be also of technological importance, since they indicate a considerably enhanced H mobility in specific structured material environments. A new INS experiment is proposed concerning the H mobility of an ultra-fast proton conductor (H${}_3$OSbTeO${}_6$) being of technological relevance. Further neutron scattering investigations on other systems (metallic hydrides and H${}_2$ encapsulated inside C${}_{60}$) are proposed. As concerns theoretical implications, the analysis of the experimental results strongly supports the view that the wavefunction (or state vector) represents an ontological physical entity of a single quantum system. Full article

Multiagent technologies provide a new way for studying and controlling complex systems. Local interactions between agents often lead to group synchronization, also known as clusterization (or clustering), which is usually a more rapid process in comparison with relatively slow changes in external environment. Usually, the goal of system control is defined by the behavior of a system on long time intervals. As is well known, a clustering procedure is generally much faster than the process of changing in the surrounding (system) environment. In this case, as a rule, the control objectives are determined by the behavior of the system at large time intervals. If the considered time interval is much larger than the time during which the clusters are formed, then the formed clusters can be considered to be “new variables” in the “slow” time model. Such variables are called “mesoscopic” because their scale is between the level of the entire system (macro-level) and the level of individual agents (micro-level). Detailed models of complex systems that consist of a large number of elementary components (miniature agents) are very difficult to control due to technological barriers and the colossal complexity of tasks due to their enormous dimension. At the level of elementary components of systems, in many applications it is impossible to verify the models of the agent dynamics with the traditionally high degree of accuracy, due to their miniaturization and high frequency of control actions. The use of new mesoscopic variables can make it possible to synthesize fewer different control inputs than when considering the system as a collection of a large number of agents, since such inputs will be common for entire clusters. In order to implement this idea, the “clusters flow” framework was formalized and used to analyze the Kuramoto model as an attracting example of a complex nonlinear networked system with the effects of opportunities for the emergence of clusters. It is shown that clustering leads to a sparse representation of the dynamic trajectories of the system, which makes it possible to apply the method of compressive sensing in order to obtain the dynamic characteristics of the formed clusters. The essence of the method is as follows. With the dimension N of the total state space of the entire system and the a priori assignment of the upper bound for the number of clusters s, only m integral randomized observations of the general state vector of the entire large system are formed, where m is proportional to the number s that is multiplied by logarithm $N/s$. A two-stage observation algorithm is proposed: first, the state space is limited and discretized, and compression then occurs directly, according to which reconstruction is then performed, which makes it possible to obtain the integral characteristics of the clusters. Based on these obtained characteristics, further, it is possible to synthesize mesocontrols for each cluster while using general model predictive control methods in a space of dimension no more than s for a given control goal, while taking the constraints obtained on the controls into account. In the current work, we focus on a centralized strategy of observations, leaving possible decentralized approaches for the future research. The performance of the new framework is illustrated with examples of simulation modeling. Full article

Geosmithia members are mitosporic filamentous fungi commonly recorded and isolated from bark beetles of the Scolytinae subfamily and their respective host’s species. This genus includes 18 species formally described and 38 phylogenetic species recorded in several localities from Africa, Asia, Australia, Europe, and North and South America, where they exhibit frequent associations with phloeophagous and wood-boring bark beetles. Among phloephagous bark beetle species, specifically, in members of the genus Phloeosinus Chapuis, almost 10% of Geosmithia strains have been isolated. By its physiographic elements and high bark beetle and conifer species richness, Mexico is a potential region to host a high diversity of Geosmithia species and potential new species. In the present study, we systematically sampled and isolated, cultured, and molecularly identified members of the Geosmithia species associated with Phloeosinus spp. and their Juniperus spp. host trees at the north of Sierra Madre Oriental, at Nuevo Leon State, Mexico. Phylogenetic analyses based on 378 internal transcribed spacer region (ITS) sequences supported the presence of strains from Geosmithia langdonii-Geosmithia sp. 32 clade associated with Phloeosinus serratus vector and with Juniperus coahuilensis (JC) host, and the presence of strains from Geosmithia sp. 21-Geosmithia xerotolerans clade with Phloeosinusdeleoni and Juniperus flaccida (JF) in this geographical region. The genetic and morphological differences found in our strains with respect to those previously described in the species from both clades (Geosmithia langdonii-Geosmithia sp. 32 and Geosmithia sp. 21-G. xerotolerans) suggest that both Geosmithia lineages from Nuevo Leon correspond to two potential new species in the genus. Full article

The Transactional Interpretation of quantum mechanics exploits the intrinsic time-symmetry of wave mechanics to interpret the $\psi$ and $\psi$* wave functions present in all wave mechanics calculations as representing retarded and advanced waves moving in opposite time directions that form a quantum “handshake” or transaction. This handshake is a 4D standing-wave that builds up across space-time to transfer the conserved quantities of energy, momentum, and angular momentum in an interaction. Here, we derive a two-atom quantum formalism describing a transaction. We show that the bi-directional electromagnetic coupling between atoms can be factored into a matched pair of vector potential Green’s functions: one retarded and one advanced, and that this combination uniquely enforces the conservation of energy in a transaction. Thus factored, the single-electron wave functions of electromagnetically-coupled atoms can be analyzed using Schrödinger’s original wave mechanics. The technique generalizes to any number of electromagnetically coupled single-electron states—no higher-dimensional space is needed. Using this technique, we show a worked example of the transfer of energy from a hydrogen atom in an excited state to a nearby hydrogen atom in its ground state. It is seen that the initial exchange creates a dynamically unstable situation that avalanches to the completed transaction, demonstrating that wave function collapse, considered mysterious in the literature, can be implemented with solutions of Schrödinger’s original wave mechanics, coupled by this unique combination of retarded/advanced vector potentials, without the introduction of any additional mechanism or formalism. We also analyze a simplified version of the photon-splitting and Freedman–Clauser three-electron experiments and show that their results can be predicted by this formalism. Full article

In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the $SU\left(2\right)$ symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections $m=\pm 1/2$ onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties. Full article

We design and investigate an original optical component made of a c-cut uniaxial crystal and an optical system to generate cylindrical vector beams with an adjustable polarization state. The original optical component has a specific, nearly conical shape which allows it to operate like a broadband wave retarder with the fast axis oriented radially with respect to the optical axis. We show via numerical simulations, using the Debye–Wolf diffraction integral, that the focal spot changes depending on the polarization state, thus enabling the control of the focal shape. Non-symmetrical shapes can be created although the optical system and incoming beam are circularly symmetric. We explained, using Jones matrix formalism, that this phenomenon is connected with the Gouy phase difference acquired by certain modes composing the beam due to propagation to the focal plane. We present our conclusions in the context of two potential applications, namely, stimulated emission depletion (STED) microscopy and laser micromachining. The optical system can potentially be used for STED microscopy for better control of the point-spread function of the microscope and to decrease the unwanted light emitted from the surroundings of the focal point. We give an analytical expression for the shape of the original component using the aspherical lens formula for the two versions of the component: one for each potential application. Full article