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We derive the mathematical condition under which the physical solution of the many-electron problem, obtained by self-consistent approaches, becomes unstable upon increasing interaction strength. The validity of our criterion is explicitly verified by performing self-consistent calculations of basic interacting models. In this context, we eventually unveiled the precise connection linking the misleading convergence of self-consistent schemes to the multivaluedness of the Luttinger-Ward functional as well as to the divergences of the irreducible vertex function. Our analysis also explains how a misleading convergence of self-consistent approximations can occur even in parameter regions without vertex divergences. Even more importantly, it allows us to define a general procedure for stabilizing the physical solution, when it is unstable in conventional self-consistent schemes.

Two major milestones on the road to the full complexity dichotomy for finite-domain constraint satisfaction problems were Bulatov's proof of the dichotomy for conservative templates, and the structural dichotomy for smooth digraphs of algebraic length 1 due to Barto, Kozik, and Niven. We lift the combined scenario to the infinite, and prove that any smooth digraph of algebraic length 1 pp-constructs, together with pairs of orbits of an oligomorphic subgroup of its automorphism group, every finite structure -- and hence its conservative graph-colouring problem is NP-hard -- unless the digraph has a pseudo-loop, i.e. an edge within an orbit. We thereby overcome, for the first time, previous obstacles to lifting structural results for digraphs in this context from finite to $\omega$-categorical structures; the strongest lifting results hitherto not going beyond a generalisation of the Hell-Ne\v{s}et\v{r}il theorem for undirected graphs. As a consequence, we obtain a new algebraic invariant of arbitrary $\omega$-categorical structures enriched by pairs of orbits which fail to pp-construct some finite structure., Comment: 27 pages

Diagrammatic expansions are a paradigmatic and powerful tool of quantum many-body theory. Their evaluation to high order, e.g., by the Diagrammatic Monte Carlo technique, can provide unbiased results in strongly correlated and challenging regimes. However, calculating a factorial number of terms to acceptable precision remains very costly even for state-of-the-art methods. We achieve a dramatic acceleration of evaluating Feynman's diagrammatic series by use of specialised hardware architecture within the recently introduced combinatorial summation (CoS) framework. We present how exploiting the massive parallelism and concurrency available from GPUs leads to orders of magnitude improvement in computation time even on consumer-grade hardware. This provides a platform for making probes of novel phenomena of strong correlations much more accessible., Comment: 11 pages, 7 figures

The fractional quantum Hall (FQH) effect arises from strong electron correlations in a quantising magnetic field, and features exotic emergent phenomena such as electron fractionalisation. Using the diagrammatic Monte Carlo approach with the combinatorial summation algorithm, we obtain results with controlled accuracy for the microscopic model of interacting electrons in the lowest Landau level. As the temperature is lowered, we study the development and emergence of the incompressible 1/3-filled FQH state. By analysing the long-time decay of the Green's function, we find spectral properties consistent with an energy gap near 1/3-filling, while at half-filling an anomalous power law scaling is observed for short-range interaction screening, indicative of a non-Fermi liquid metal. Our work provides the first demonstration that fractionalised phases of matter can be reliably described with Feynman's diagrammatic technique in terms of the fundamental electronic degrees of freedom, while also showing applicability of expansions in the bare Coulomb potential for precision calculations., Comment: 8 pages, 2 figures

In this work we provide a model-independent experimental evaluation of the degree of isospin equilibration taking place in $^{58,64}$Ni+$^{58,64}$Ni collisions at 32 MeV/nucleon across varying reaction centralities. This result has been obtained by combining the complementary information provided by two different datasets, sharing common characteristics. The first dataset has been acquired with the INDRA setup and has been used to implement a model-independent reconstruction of the impact parameter. The second dataset has been acquired in the first experimental campaign of the coupled INDRA-FAZIA apparatus at GANIL. The neutron-to-proton content of the quasiprojectile remnant measured by FAZIA has been employed as isospin observable. The effect of isospin diffusion has been evidenced by means of the isospin transport ratio, reported as a function of the impact parameter of the collision. The evolution towards isospin equilibration from semiperipheral to more central collisions is clearly extracted. This experimental result, expanding our previous works (Phys. Rev. C 106, 024603 (2022) and Phys. Rev. C 108, 054611 (2023)), can be compared with the predictions of any transport model, and can thus be used to set constraints on the behavior of the symmetry energy term of the nuclear Equation of State at sub- to saturation densities.

Positron Annihilation Lifetime Spectroscopy (PALS) is a well-established non-destructive technique used for nanostructural characterization of porous materials. It is based on the annihilation of a positron and an electron. Mean positron lifetime in the material depends on the free voids size and molecular environment, allowing the study of porosity and structural transitions in the nanometer scale. We have developed a novel method enabling spatially resolved PALS, thus providing tomography of nanostructural characterization of an extended object. Correlating space (position) and structural (lifetime) information brings new insight in materials studies, especially in the characterization of the purity and pore distribution. For the first time, a porosity image using stationary positron sources for the simultaneous measurement of the porous polymers XAD4, silica aerogel powder IC3100, and polyvinyl toluene scintillator PVT by the J-PET tomograph is demonstrated

We give a new, direct proof of the tetrachotomy classification for the model-checking problem of positive equality-free logic parameterised by the model. The four complexity classes are Logspace, NP-complete, co-NP-complete and Pspace-complete. The previous proof of this result relied on notions from universal algebra and core-like structures called U-X-cores. This new proof uses only relations, and works for infinite structures also in the distinction between Logspace and NP-hard under Turing reductions. For finite domains, the membership in NP and co-NP follows from a simple argument, which breaks down already over an infinite set with a binary relation. We develop some interesting new algorithms to solve NP and co-NP membership for a variety of infinite structures. We begin with those first-order definable in (Q;=), the so-called equality languages, then move to those first-order definable in (Q;<), the so-called temporal languages. However, it is first-order expansions of the Random Graph (V,E) that provide the most interesting examples. In all of these cases, the derived classification is a tetrachotomy between Logspace, NP-complete, co-NP-complete and Pspace-complete.

The growing interest in human-grade total body positron emission tomography (PET) systems has also application in small animal research. Due to the existing limitations in human-based studies involving drug development and novel treatment monitoring, animal-based research became a necessary step for testing and protocol preparation. In this simulation-based study two unconventional, cost-effective small animal total body PET scanners (for mouse and rat studies) have been investigated in order to inspect their feasibility for preclinical research. They were designed with the novel technology explored by the Jagiellonian-PET (J-PET) Collaboration. Two main PET characteristics: sensitivity and spatial resolution were mainly inspected to evaluate their performance. Moreover, the impact of the scintillator dimension and time-of-flight on the latter parameter was examined in order to design the most efficient tomographs. The presented results show that for mouse TB J-PET the achievable system sensitivity is equal to 2.35% and volumetric spatial resolution to 9.46 +- 0.54 mm3, while for rat TB J-PET they are equal to 2.6% and 14.11 +- 0.80 mm3, respectively. Furthermore, it was shown that the designed tomographs are almost parallax-free systems, hence, they resolve the problem of the acceptance criterion tradeoff between enhancing spatial resolution and reducing sensitivity.

Plastic scintillator strips are considered as one of the promising solutions for the cost-effective construction of total-body positron emission tomography, (PET) system. The purpose of the performed measurements is to compare the transparency of long plastic scintillators with dimensions 6 mm x 24 mm x 1000 mm and with all surfaces polished. Six different types of commercial, general purpose, blue-emitting plastic scintillators with low attenuation of visible light were tested, namely: polyvinyl toluene-based BC-408, EJ-200, RP-408, and polystyrene-based Epic, SP32 and UPS-923A. For determination of the best type of plastic scintillator for totalbody Jagiellonian positron emission tomograph (TB-J-PET) construction, emission and transmission spectra, and technical attenuation length (TAL) of blue light-emitting by the scintillators were measured and compared. The TAL values were determined with the use of UV lamp as excitation source, and photodiode as light detector. Emission spectra of investigated scintillators have maxima in the range from 420 nm to 429 nm. The BC-408 and EJ-200 have the highest transmittance values of about 90% at the maximum emission wavelength measured through a 6 mm thick scintillator strip and the highest technical attenuation length reaching about 2000 mm, allowing assembly of long detection modules for time-of-flight (TOF) J-PET scanners. Influence of the 6 mm x 6 mm, 12 mm x 6 mm, 24 mm x 6 mm cross-sections of the 1000 mm long EJ-200 plastic scintillator on the TAL and signal intensity was measured. The highest TAL value was determined for samples with 24 mm x 6 mm cross-section., Comment: 10 pages, 5 figures

In the state-of-the-art Positron Emission Tomography (PET), information about the polarization of annihilation photons is not available. Current PET systems track molecules labeled with positron-emitting radioisotopes by detecting the propagation direction of two photons from positron-electron annihilation. However, annihilation photons carry more information than just the site where they originated. Here we present a novel J-PET scanner built from plastic scintillators, in which annihilation photons interact predominantly via the Compton effect, providing information about photon polarization in addition to information on photon direction of propagation. Theoretically, photons from the decay of positronium in a vacuum are maximally entangled in polarization. However, in matter, when the positron from positronium annihilates with the electron bound to the atom, the question arises whether the photons from such annihilation are maximally entangled. In this work, we determine the distribution of the relative angle between polarization orientations of two photons from positron-electron annihilation in a porous polymer. Contrary to prior results for positron annihilation in aluminum and copper, where the strength of observed correlations is as expected for maximally entangled photons, our results show a significant deviation. We demonstrate that in porous polymer, photon polarization correlation is weaker than for maximally entangled photons but stronger than for separable photons. The data indicate that more than 40% of annihilations in Amberlite resin lead to a non-maximally entangled state. Our result indicates the degree of correlation depends on the annihilation mechanism and the molecular arrangement. We anticipate that the introduced Compton interaction-based PET system opens a promising perspective for exploring polarization correlations in PET as a novel diagnostic indicator.

We present a template for the Promise Constraint Satisfaction Problem (PCSP) which is NP-hard but does not satisfy the current state-of-the-art hardness condition [ACMTCT'21]. We introduce a new "injective" condition based on the smooth version of the layered PCP Theorem and use this new condition to confirm that the problem is indeed NP-hard. In the second part of the article, we establish a dichotomy for Boolean PCSPs defined by templates with polymorphisms in the set of linear threshold functions. The reasoning relies on the new injective condition., Comment: To be published in LICS'24

The emission of the pre-equilibrium particles during nuclear collisions at moderate beam energies is still an open question. This influences the properties of the compound nucleus but also changes the interpretation of the quasi-fission process. A systematic analysis of the data obtained by the FAZIA collaboration during a recent experiment with a neutron rich projectile is presented. The full range of charged particles detected in the experiment is within the limit of isotopic resolution of the FAZIA detector. Quasi-projectile (QP) fragments were detected in majority thanks to the forward angular acceptance of the experimental setup which was confirmed by introducing cuts based on the HIPSE event generator calculations. The main goal was to compare the experimental results with the HIPSE simulations after introducing these cuts to investigate the influence of the n-rich entrance channel on the QP fragment properties. More specifically, the lowering of N/Z of QP fragments with beam energy was found to be present since the initial phase of the reaction. Thus, pre-equilibrium emissions might be a possible candidate to explain such an effect., Comment: 10 pages, 10 figures

Discrete symmetries play an important role in particle physics with violation of CP connected to the matter-antimatter imbalance in the Universe. We report the most precise test of P, T and CP invariance in decays of ortho-positronium, performed with methodology involving polarization of photons from these decays. Positronium, the simplest bound state of an electron and positron, is of recent interest with discrepancies reported between measured hyperfine energy structure and theory at the level of $10^{-4}$ signaling a need for better understanding of the positronium system at this level. We test discrete symmetries using photon polarizations determined via Compton scattering in the dedicated J-PET tomograph on an event-by-event basis and without the need to control the spin of the positronium with an external magnetic field, in contrast to previous experiments. Our result is consistent with QED expectations at the level of 0.0007 and one standard deviation., Comment: 17 pages, 10 figures

This article presents an investigation of isospin equilibration in cross-bombarding $^{40,48}$Ca$+^{40,48}$Ca reactions at 35 MeV/nucleon, by comparing experimental data with filtered transport model calculations. Isospin diffusion is studied using the evolution of the isospin transport ratio with centrality. The asymmetry parameter $\delta=(N-Z)/A$ of the quasiprojectile (QP) residue is used as isospin-sensitive observable, while a recent method for impact parameter reconstruction is used for centrality sorting. A benchmark of global observables is proposed to assess the relevance of the antisymmetrized molecular dynamics (AMD) model, coupled to GEMINI++, in the study of dissipative collisions. Our results demonstrate the importance of considering cluster formation to reproduce observables used for isospin transport and centrality studies. Within the AMD model, we prove the applicability of the impact parameter reconstruction method, enabling a direct comparison to the experimental data for the investigation of isospin diffusion. For both, we evidence a tendency to isospin equilibration with an impact parameter decreasing from 9 to 3 fm, while the full equilibration is not reached. A weak sensitivity to the stiffness of the equation of state employed in the model is also observed, with a better reproduction of the experimental trend for the neutron-rich reactions.

We study the microscopic model of electrons in the partially-filled lowest Landau level interacting via the Coulomb potential by the diagrammatic theory within the GW approximation. In a wide range of filling fractions and temperatures, we find a homogeneous non-Fermi liquid (nFL) state similar to that found in the Sachdev-Ye-Kitaev (SYK) model, with logarithmic corrections to the anomalous dimension. In addition, the phase diagram is qualitatively similiar to that of SYK: a first-order transition terminating at a critical end-point separates the nFL phase from a band insulator that corresponds to the fully-filled Landau level. This critical point, as well as that of the SYK model -- whose critical exponents we determine more precisely -- are shown to both belong to the Van der Waals universality class. The possibility of a charge density wave (CDW) instability is also investigated, and we find the homogeneous nFL state to extend down to the ground state for fillings $0.2 \lesssim \nu \lesssim 0.8$, while a CDW appears outside this range of fillings at sufficiently low temperatures. Our results suggest that the SYK-like nFL state should be a generic feature of the partially-filled lowest Landau level at intermediate temperatures., Comment: 11+6 pages, 6 figures

Feynman's diagrammatic series is a common language for a formally exact theoretical description of systems of infinitely-many interacting quantum particles, as well as a foundation for precision computational techniques. Here we introduce a universal framework for efficient summation of connected or skeleton Feynman diagrams for generic quantum many-body systems. It is based on an explicit combinatorial construction of the sum of the integrands by dynamic programming, at a computational cost that can be made only exponential in the diagram order on a classical computer and potentially polynomial on a quantum computer. We illustrate the technique by an unbiased diagrammatic Monte Carlo calculation of the equation of state of the $2D$ $SU(N)$ Hubbard model in an experimentally relevant regime, which has remained challenging for state-of-the-art numerical methods., Comment: 10 pages, 5 figures

Studies based on imaging the annihilation of the electron (e$^{-}$) and its antiparticle positron (e$^{+}$) open up several interesting applications in nuclear medicine and fundamental research. The annihilation process involves both the direct conversion of e$^{+}$e$^{-}$ into photons and the formation of their atomically bound state, the positronium atom (Ps), which can be used as a probe for fundamental studies. With the ability to produce large quantities of Ps, manipulate them in long-lived Ps states, and image their annihilations after a free fall or after passing through atomic interferometers, this purely leptonic antimatter system can be used to perform inertial sensing studies in view of a direct test of Einstein equivalence principle. It is envisioned that modular multistrip detectors can be exploited as potential detection units for this kind of studies. In this work, we report the results of the first feasibility study performed on a e$^{+}$ beamline using two detection modules to evaluate their reconstruction performance and spatial resolution for imaging e$^{+}$e$^{-}$ annihilations and thus their applicability for gravitational studies of Ps.

An investigation of the quasiprojectile breakup channel in semiperipheral and peripheral collisions of $^{58,64}$Ni+$^{58,64}$Ni at 32 and 52 MeV/nucleon is presented. Data have been acquired in the first experimental campaign of the INDRA-FAZIA apparatus in GANIL. The effect of isospin diffusion between projectile and target in the two asymmetric reactions has been highlighted by means of the isospin transport ratio technique, exploiting the neutron-to-proton ratio of the quasiprojectile reconstructed from the two breakup fragments. We found evidence that, for the same reaction centrality, a higher degree of relaxation of the initial isospin imbalance is achieved in the breakup channel with respect to the more populated binary output, possibly indicating the indirect selection of specific dynamical features. We have proposed an interpretation based on different average projectile-target contact times related to the two exit channels under investigation, with a longer interaction for the breakup channel. The time information has been extracted from AMD simulations of the studied systems coupled to GEMINI++: the model calculations support the hypothesis hereby presented.

We investigate local computation algorithms (LCA) for two-coloring of $k$-uniform hypergraphs. We focus on hypergraph instances that satisfy strengthened assumption of the Lov\'{a}sz Local Lemma of the form $2^{1-\alpha k} (\Delta+1) \mathrm{e} < 1$, where $\Delta$ is the bound on the maximum edge degree. The main question which arises here is for how large $\alpha$ there exists an LCA that is able to properly color such hypergraphs in polylogarithmic time per query. We describe briefly how upgrading the classical sequential procedure of Beck from 1991 with Moser and Tardos' RESAMPLE yields polylogarithmic LCA that works for $\alpha$ up to $1/4$. Then, we present an improved procedure that solves wider range of instances by allowing $\alpha$ up to $1/3$., Comment: Full version of the paper accepted for the ICALP 2023 conference (additional appendixes B, C, D)

Background: Total-Body imaging offers high sensitivity, single-bed position, and low dose, but high construction costs limit worldwide utilization. This study compares existing and developing tomographs using plastic scintillators via simulations to propose a cost-efficient Total-Body PET scanner. Methods: Simulations of eight uEXPLORER tomographs with different scintillator materials, axial field-of-view, and detector configuration, and eight J-PET scanners with various field-of-view, plastic scintillator cross-sections, and layers were performed. Biograph Vision was also simulated. Two types of simulations were conducted with a central source and a water-filled phantom. Results: BGO crystal-based scanners showed the best sensitivity (350 cps/kBq at the center). Sparse geometry or LYSO crystals reduced sensitivity. J-PET design showed similar sensitivity to sparse LYSO detectors, with full body coverage and additional gain for brain imaging. Conclusion: The J-PET tomography system using plastic scintillators could be a cost-efficient alternative for Total-Body PET scanners, overcoming high construction costs while maintaining sensitivity

Four different reactions, $^{32}$S+$^{12}$C and $^{20}$Ne+$^{12}$C at 25 and 50 MeV/nucleon, have been measured with the FAZIA detector capable of full isotopic identification of most forward emitted reaction products. Fragment multiplicities, angular distributions and energy spectra have been measured and compared with Monte Carlo simulations, i.e. the antisymmetrized molecular dynamics (AMD) and the heavy-ion phase space exploration (HIPSE) models. These models are combined with two different afterburner codes (HF$l$ and SIMON) to describe the decay of the excited primary fragments. In the case of AMD, the effect of including the clustering and inter-clustering processes to form bound particles and fragments is discussed. A clear confirmation of the role of cluster aggregation in the reaction dynamics and particle production for these light systems, for which the importance of the clustering process increases with bombarding energy, is obtained., Comment: 15 pages, 14 PDF figures

An analysis of the asymmetric reactions $^{40,48}$Ca+$^{12}$C at 25 and 40 MeV/nucleon is presented. Data have been collected with six modules of the FAZIA array. The analysis is focused on the breakup channel of sources produced in dissipative collisions, partially corresponding to incomplete fusion processes. The study has been performed both on detected fragments and on some resonances reconstructed by means of particle-fragment correlations, with a focus on the evolution of the breakup channel with the beam energy and the neutron content of the system, looking in particular at the relative velocity between the breakup fragments. Results show that also Carbon fragments reconstructed by means of particle correlations can be in large part interpreted as the light partner of a scission.

Thomassen in 1994 published a famous proof of the fact that the choosability of a planar graph is at most 5. Zhu in 2019 generalized this result by showing that the same bound holds for Alon-Tarsi numbers of planar graphs. We present an alternative proof of that fact, derived from the results on decompositions of planar graphs into trees known as Schnyder woods. It turns out that Thomassen's technique and our proof based on Schnyder woods have a lot in common. We discuss and explain the prominent role that counterclockwise 3-orientations play in proofs based on both these approaches.

Objective: The aim of this work is to investigate the feasibility of the Jagiellonian Positron Emission Tomography (J-PET) scanner for intra-treatment proton beam range monitoring. Approach: The Monte Carlo simulation studies with GATE and PET image reconstruction with CASToR were performed in order to compare six J-PET scanner geometries (three dual-heads and three cylindrical). We simulated proton irradiation of a PMMA phantom with a Single Pencil Beam (SPB) and Spread-Out Bragg Peak (SOBP) of various ranges. The sensitivity and precision of each scanner were calculated, and considering the setup's cost-effectiveness, we indicated potentially optimal geometries for the J-PET scanner prototype dedicated to the proton beam range assessment. Main results: The investigations indicate that the double-layer cylindrical and triple-layer double-head configurations are the most promising for clinical application. We found that the scanner sensitivity is of the order of 10$^{-5}$ coincidences per primary proton, while the precision of the range assessment for both SPB and SOBP irradiation plans was found below 1 mm. Among the scanners with the same number of detector modules, the best results are found for the triple-layer dual-head geometry. Significance: We performed simulation studies demonstrating that the feasibility of the J-PET detector for PET-based proton beam therapy range monitoring is possible with reasonable sensitivity and precision enabling its pre-clinical tests in the clinical proton therapy environment. Considering the sensitivity, precision and cost-effectiveness, the double-layer cylindrical and triple-layer dual-head J-PET geometry configurations seem promising for the future clinical application. Experimental tests are needed to confirm these findings., Comment: 19 pages, 7 pages

We investigate structural implications arising from the condition that a given directed graph does not interpret, in the sense of primitive positive interpretation with parameters or orbits, every finite structure. Our results generalize several theorems from the literature and yield further algebraic invariance properties that must be satisfied in every such graph. Algebraic properties of this kind are tightly connected to the tractability of constraint satisfaction problems, and we obtain new such properties even for infinite countably categorical graphs. We balance these positive results by showing the existence of a countably categorical hypergraph that fails to interpret some finite structure, while still lacking some of the most essential algebraic invariance properties known to hold for finite structures.

The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we investigate this constraint satisfaction problem in a regime where the promise is weakened from either side by a rainbow-free structure, and establish a complexity dichotomy for the resulting class of computational problems., Comment: Full version of a LICS 2024 paper

We report a study of the original image reconstruction algorithm based on the time-of-flight maximum likelihood expectation maximisation (TOF MLEM), developed for the total-body (TB) Jagiellonian PET (J-PET) scanners. The method is applicable to generic cylindrical or modular multi-layer layouts and is extendable to multi-photon imaging. The system response matrix (SRM) is represented as a set of analytical functions, uniquely defined for each pair of plastic scintillator strips used for the detection. A realistic resolution model (RM) in detector space is derived from fitting the Monte Carlo simulated emissions and detections of annihilation photons on oblique transverse planes. Additional kernels embedded in SRM account for TOF, parallax effect and axial smearing. The algorithm was tested on datasets, simulated in GATE for the NEMA IEC and static XCAT phantoms inside a 24-module 2-layer TB J-PET. Compared to the reference TOF MLEM with none or a shift-invariant RM, an improvement was observed, as evaluated by the analysis of image quality, difference images and ground truth metrics. We also reconstructed the data with additive contributions, pre-filtered geometrically and with non-TOF scatter correction applied. Despite some deterioration, the obtained results still capitalise on the realistic RM with better edge preservation and superior ground truth metrics. The envisioned prospects of the TOF MLEM with analytical SRM include its application in multi-photon imaging and further upgrade to account for the non-collinearity, positron range and other factors.

The J-PET detector, which consists of inexpensive plastic scintillators, has demonstrated its potential in the study of fundamental physics. In recent years, a prototype with 192 plastic scintillators arranged in 3 layers has been optimized for the study of positronium decays. This allows performing precision tests of discrete symmetries (C, P, T) in the decays of positronium atoms. Moreover, thanks to the possibility of measuring the polarization direction of the photon based on Compton scattering, the predicted entanglement between the linear polarization of annihilation photons in positronium decays can also be studied. Recently, a new J-PET prototype was commissioned, based on a modular design of detection units. Each module consists of 13 plastic scintillators and can be used as a stand-alone, compact and portable detection unit. In this paper, the main features of the J-PET detector, the modular prototype and their applications for possible studies with positron and positronium beams are discussed. Preliminary results of the first test experiment performed on two detection units in the continuous positron beam recently developed at the Antimatter Laboratory (AML) of Trento are also reported.

Convergence of the self-consistent skeleton diagrammatic technique (SDT) -- in which the full Green's function is determined through summation of Feynman diagrams in terms of itself -- to the wrong answer has been associated with the existence of non-perturbative branches of the Luttinger-Ward functional. Although it has been possible to detect misleading convergence without the knowledge of the exact result, the SDT has remained inapplicable in the regimes where this happens. We show that misleading convergence does not always preclude recovering the exact solution. In addition to the established mechanism, convergence of the SDT to the wrong answer can stem from divergence of the inherent diagrammatic series, which allows us to recover the exact solution by a modified SDT protocol based on controlled analytic continuation. We illustrate this approach by its application to the analytically solvable (0+0)d Hubbard model, the Hubbard atom, and the 2d Hubbard model in a challenging strong-coupling regime, for which the SDT is solved with controlled accuracy by the diagrammatic Monte Carlo (DiagMC) technique., Comment: 6 pages, 5 figures

The vision of 2030STEM is to address systemic barriers in institutional structures and funding mechanisms required to achieve full inclusion in Science, Technology, Engineering, and Mathematics (STEM) and provide leadership opportunities for individuals from underrepresented populations across STEM sectors. 2030STEM takes a systems-level approach to create a community of practice that affirms diverse cultural identities in STEM. This is the first in a series of white papers based on 2030STEM Salons - discussions that bring together visionary stakeholders in STEM to think about innovative ways to infuse justice, equity, diversity, and inclusion into the STEM ecosystem. Our salons identify solutions that come from those who have been most affected by systemic barriers in STEM. Our first salon focused on the power of social media to accelerate inclusion and diversity efforts in STEM. Social media campaigns, such as the #XinSTEM initiatives, are powerful new strategies for accelerating change towards inclusion and leadership by underrepresented communities in STEM. This white paper highlights how #XinSTEM campaigns are redefining community, and provides recommendations for how scientific and funding institutions can improve the STEM ecosystem by supporting the #XinSTEM movement., Comment: 13 pages, 2 Figures

Total-Body PET is one of the most promising medical diagnostics modalities. The high sensitivity provided by Total-Body technology can be advantageous for novel tomography methods like positronium imaging. Several efforts are ongoing to lower the price of the TB-PET systems. Among the alternatives, the Jagiellonian PET (J-PET) technology, based on plastic scintillator strips, offers a low-cost alternative. The work aimed to compare five Total-Body J-PET geometries as a possible next generation J-PET scanner design. We present comparative studies of performance characteristics of the cost-effective Total-Body PET scanners using J-PET technology. We investigated in silico five Total-Body scanner geometries. Monte Carlo simulations of the XCAT phantom, the 2-meter sensitivity line source and positronium sensitivity phantoms were performed. We compared the sensitivity profiles for 2-gamma and 3-gamma tomography, relative cost of the setups and performed quantitative analysis of the reconstructed images. The analysis of the reconstructed XCAT images reveals the superiority of the seven-ring scanners over the three-ring setups. However, the three-ring scanners would be approximately 2-3 times cheaper. The peak sensitivity values for two-gamma vary from 20 to 34 cps/kBq. The sensitivity curves for the positronium tomography have a similar shape to the two-gamma sensitivity profiles. The peak values are lower compared to the two-gamma cases, from about 20-28 times, with a maximum of 1.66 cps/kBq. The results show the feasibility of multi-organ imaging of all the systems to be considered for the next generation of TB J-PET designs. The relative cost for all the scanners is about 10-4 times lower compared to the cost of the uExplorer. These properties coupled together with J-PET cost-effectiveness, make the J-PET technology an attractive solution for broad application in clinics.

An investigation of the isospin equilibration process in the reactions $^{58,64}$Ni+$^{58,64}$Ni at two bombarding energies in the Fermi regime ($32\,$MeV/nucleon and $52\,$MeV/nucleon) is presented. Data have been acquired during the first experimental campaign of the coupled INDRA-FAZIA apparatus in GANIL. Selecting from peripheral to semi-central collisions, both the neutron content of the quasiprojectile residue and that of the light ejectiles coming from the quasiprojectile evaporation have been used as probes of the dynamical process of isospin diffusion between projectile and target for the asymmetric systems. The isospin transport ratio technique has been employed. The relaxation of the initial isospin imbalance with increasing centrality has been clearly evidenced. The isospin equilibration appears stronger for the reactions at $32\,$MeV/nucleon, as expected due to the longer projectile-target interaction time than at $52\,$MeV/nucleon. Coherent indications of isospin equilibration come from the quasiprojectile residue characteristics and from particles ascribed to the quasiprojectile decay.

Diagrammatic Monte Carlo -- the technique for numerically exact summation of all Feynman diagrams to high orders -- offers a unique unbiased probe of continuous phase transitions. Being formulated directly in the thermodynamic limit, the diagrammatic series is bound to diverge and is not resummable at the transition due to the non-analyticity of physical observables. This enables the detection of the transition with controlled error bars from an analysis of the series coefficients alone, avoiding the challenge of evaluating physical observables near the transition. We demonstrate this technique by the example of the N\'eel transition in the $3d$ Hubbard model. At half-filling and higher temperatures, the method matches the accuracy of state-of-the-art finite-size techniques, but surpasses it at low temperatures and allows us to map the phase diagram in the doped regime, where finite-size techniques struggle from the fermion sign problem. At low temperatures and sufficient doping, the transition to an incommensurate spin density wave state is observed.

In vivo assessment of cancer and precise location of altered tissues at initial stages of molecular disorders are important diagnostic challenges. Positronium is copiously formed in the free molecular spaces in the patient's body during positron emission tomography (PET). The positronium properties vary according to the size of inter- and intramolecular voids and the concentration of molecules in them such as, e.g., molecular oxygen, O2; therefore, positronium imaging may provide information about disease progression during the initial stages of molecular alterations. Current PET systems do not allow acquisition of positronium images. This study presents a new method that enables positronium imaging by simultaneous registration of annihilation photons and deexcitation photons from pharmaceuticals labeled with radionuclides. The first positronium imaging of a phantom built from cardiac myxoma and adipose tissue is demonstrated. It is anticipated that positronium imaging will substantially enhance the specificity of PET diagnostics., Comment: 10 pages, 5 figures

Charged lepton system symmetry under combined charge, parity, and time-reversal transformation (CPT) remains scarcely tested. Despite stringent quantum-electrodynamic limits, discrepancies in predictions for the electron-positron bound state (positronium atom) motivate further investigation, including fundamental symmetry tests. While CPT noninvariance effects could be manifested in non-vanishing angular correlations between final-state photons and spin of annihilating positronium, measurements were previously limited by knowledge of the latter. Here, we demonstrate tomographic reconstruction techniques applied to three-photon annihilations of ortho-positronium atoms to estimate their spin polarisation without magnetic field or polarised positronium source. We use a plastic-scintillator-based positron-emission-tomography scanner to record ortho-positronium (o-Ps) annihilations with single-event estimation of o-Ps spin and determine the complete spectrum of an angular correlation operator sensitive to CPT-violating effects. We find no violation at the precision level of 10^{-4}, with an over threefold improvement on the previous measurement., Comment: This is a preprint of an article published in Nature Communications. The final version is available at https://rdcu.be/cCQqq

The discovery of Behavior Trees (BTs) impacted the field of Artificial Intelligence (AI) in games, by providing flexible and natural representation of non-player characters (NPCs) logic, manageable by game-designers. Nevertheless, increased pressure on ever better NPCs AI-agents forced complexity of handcrafted BTs to became barely-tractable and error-prone. On the other hand, while many just-launched on-line games suffer from player-shortage, the existence of AI with a broad-range of capabilities could increase players retention. Therefore, to handle above challenges, recent trends in the field focused on automatic creation of AI-agents: from deep- and reinforcementlearning techniques to combinatorial (constrained) optimization and evolution of BTs. In this paper, we present a novel approach to semi-automatic construction of AI-agents, that mimic and generalize given human gameplays by adapting and tuning of expert-created BT under a developed similarity metric between source and BT gameplays. To this end, we formulated mixed discrete-continuous optimization problem, in which topological and functional changes of the BT are reflected in numerical variables, and constructed a dedicated hybrid-metaheuristic. The performance of presented approach was verified experimentally in a prototype real-time strategy game. Carried out experiments confirmed efficiency and perspectives of presented approach, which is going to be applied in a commercial game.

A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an unsolvable instance is bounded away from one; we call this fact a gap theorem. We show that the gap theorem implies NP-hardness of a gap version of the Layered Label Cover Problem. The same result can be derived from the PCP Theorem, but a full, self-contained proof of our reduction is quite short and the result can still provide PCP-free NP-hardness proofs for numerous problems. The simplicity of our reasoning also suggests that weaker versions of Unique-Games-type conjectures, e.g., the d-to-1 conjecture, might be accessible and serve as an intermediate step for proving these conjectures in their full strength. As the second, main application we provide a sufficient condition under which a fixed template Promise Constraint Satisfaction Problem (PCSP) reduces to another PCSP. The correctness of the reduction hinges on the gap theorem, but the reduction itself is very simple. As a consequence, we obtain that every CSP can be canonically reduced to most of the known NP-hard PCSPs, such as the approximate hypergraph coloring problem.

This paper focuses on the algebraic theory underlying the study of the complexity and the algorithms for the Constraint Satisfaction Problem (CSP). We unify, simplify, and extend parts of the three approaches that have been developed to study the CSP over finite templates -- absorption theory that was used to characterize CSPs solvable by local consistency methods (JACM'14), and Bulatov's and Zhuk's theories that were used for two independent proofs of the CSP Dichotomy Theorem (FOCS'17, JACM'20). As the first contribution we present an elementary theorem about primitive positive definability and use it to obtain the starting points of Bulatov's and Zhuk's proofs as corollaries. As the second contribution we propose and initiate a systematic study of minimal Taylor algebras. This class of algebras is broad enough that it suffices to verify the CSP Dichotomy Theorem on this class only, but still is unusually well behaved. In particular, many concepts from the three approaches coincide in this class, which is in striking contrast with the general setting. We believe that the theory initiated in this paper will eventually result in a simple and more natural proof of the Dichotomy Theorem that employs a simpler and more efficient algorithm, and will help in attacking complexity questions in other CSP-related problems.

We present a progress on local computation algorithms for two coloring of $k$-uniform hypergraphs. We focus on instances that satisfy strengthened assumption of Local Lemma of the form $2^{1-\alpha k} (\Delta+1) e < 1$, where $\Delta$ is the bound on the maximum edge degree of the hypergraph. We discuss how previous works on the subject can be used to obtain an algorithm that works in polylogarithmic time per query for $\alpha$ up to about $0.139$. Then, we present a procedure that, within similar bounds on running time, solves wider range of instances by allowing $\alpha$ at most about $0.227$.