Heisenberg models and a particular isotropic model

The Heisenberg model, a quantum mechanical analogue of the Ising model, has a large ground state degeneracy, due to the symmetry generated by the total spin. This symmetry is also responsible for degeneracies in the rest of the spectrum. We discuss the global structure of the spectrum of Heisenberg models with arbitrary couplings, using group theoretical methods. The Hilbert space breaks up in blocks characterized by the quantum numbers of the total spin, $S$ and $M$, and each block is shown to constitute the representation space of an explicitly given irreducible representation of the symmetric group $S_N$, consisting of permutations of the $N$ spins in the system. In the second part of the paper we consider, as a concrete application, the model where each spin is coupled to all the other spins with equal strength. Its partition function is written as a single integral, elucidating its $N$-dependence. This provides a useful framework for studying finite size effects. We give explicit results for the heat capacity, revealing interesting behavior just around the phase transition.Comment: 16 pages LaTeX, one of the 2 figures included as a postscript file. Oxford preprint OUTP-93-18S, to be published in Phys. Rev.

Criticality in a Vlasov-Poisson system - a fermionic universality class

A model Vlasov--Poisson system is simulated close the point of marginal stability, thus assuming only the wave-particle resonant interactions are responsible for saturation, and shown to obey the power--law scaling of a second-order phase transition. The set of critical exponents analogous to those of the Ising universality class is calculated and shown to obey the Widom and Rushbrooke scaling and Josephson's hyperscaling relations at the formal dimensionality $d=5$ below the critical point at nonzero order parameter. However, the two-point correlation function does not correspond to the propagator of Euclidean quantum field theory, which is the Gaussian model for the Ising universality class. Instead it corresponds to the propagator for the fermionic {\it vector} field and to the {\it upper critical dimensionality} $d_c=2$. This suggests criticality of collisionless Vlasov-Poisson systems as representative of the {\it universality class} of critical phenomena of {\it a fermionic} quantum field description.Comment: 10 pages, 6 figures, Submitted to Phys. Rev.

Liquid-Liquid Phase Transitions for Soft-Core Attractive Potentials

Using event driven molecular dynamics simulations, we study a three dimensional one-component system of spherical particles interacting via a discontinuous potential combining a repulsive square soft core and an attractive square well. In the case of a narrow attractive well, it has been shown that this potential has two metastable gas-liquid critical points. Here we systematically investigate how the changes of the parameters of this potential affect the phase diagram of the system. We find a broad range of potential parameters for which the system has both a gas-liquid critical point and a liquid-liquid critical point. For the liquid-gas critical point we find that the derivatives of the critical temperature and pressure, with respect to the parameters of the potential, have the same signs: they are positive for increasing width of the attractive well and negative for increasing width and repulsive energy of the soft core. This result resembles the behavior of the liquid-gas critical point for standard liquids. In contrast, for the liquid-liquid critical point the critical pressure decreases as the critical temperature increases. As a consequence, the liquid-liquid critical point exists at positive pressures only in a finite range of parameters. We present a modified van der Waals equation which qualitatively reproduces the behavior of both critical points within some range of parameters, and give us insight on the mechanisms ruling the dependence of the two critical points on the potential's parameters. The soft core potential studied here resembles model potentials used for colloids, proteins, and potentials that have been related to liquid metals, raising an interesting possibility that a liquid-liquid phase transition may be present in some systems where it has not yet been observed.Comment: 29 pages, 15 figure

Correlation property of length sequences based on global structure of complete genome

This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences. The values of the exponents from these methods of these three kinds of length sequences of bacteria indicate that the long-range correlations exist in most of these sequences. The correlation have a rich variety of behaviours including the presence of anti-correlations. Further more, using the exponent $\gamma$, it is found that these correlations are all linear ($\gamma=1.0\pm 0.03$). It is also found that these sequences exhibit $1/f$ noise in some interval of frequency ($f>1$). The length of this interval of frequency depends on the length of the sequence. The shape of the periodogram in $f>1$ exhibits some periodicity. The period seems to depend on the length and the complexity of the length sequence.Comment: RevTex, 9 pages with 5 figures and 3 tables. Phys. Rev. E Jan. 1,2001 (to appear

Multimodality Treatment Improves Locoregional Control, Progression-Free and Overall Survival in Patients with Anaplastic Thyroid Cancer:A Retrospective Cohort Study Comparing Oncological Outcomes and Morbidity between Multimodality Treatment and Limited Treatment (May, 10.1245/s10434-021-10146-3, 2021)

Background: Patients with anaplastic thyroid cancer (ATC) have poor overall survival, and the optimal management approach remains unclear. The aim of this study is to evaluate our experience with multimodality (MMT) versus limited treatment (LT) for ATC. Patients and Methods: A cohort study of patients with ATC managed in a tertiary referral center was undertaken. The outcomes of MMT were compared with those of LT. The primary outcome measures were locoregional control and progression-free and overall survival. Secondary outcome measures were treatment-related complications and factors associated with improved survival. Results: In total, 59 patients (35 females) with a median age of 73 years (range 39-99 years) and ATC stage IVA (n = 2), IVB (n = 28), or IVC (n = 29) were included. LT was utilized in 25 patients (42%), and 34 cases had MMT. MMT patients had a longer time of locoregional control (18.5 versus 1.9 months; p < 0.001), progression-free survival (3.5 versus 1.2 months; p < 0.001), and overall survival (6.9 versus 2.0 months; p < 0.001) when compared with LT. For patients with stage IVC ATC, locoregional control (p = 0.03), progression-free survival (p < 0.001), and overall survival (p < 0.001) were superior in the MMT cohort compared with LT. MMT had more treatment-related complications than LT (p < 0.001). An Eastern Cooperative Oncology Group performance status < 2 (HR 0.30; p = 0.001) and MMT (HR 0.35; p = 0.008) were associated with improved overall survival. Conclusion: MMT is likely to improve locoregional control, progression-free survival, and overall survival in selected ATC patients including stage IVC tumors but comes with a greater complication risk

Multimodality Treatment Improves Locoregional Control, Progression-Free and Overall Survival in Patients with Anaplastic Thyroid Cancer:A Retrospective Cohort Study Comparing Oncological Outcomes and Morbidity between Multimodality Treatment and Limited Treatment

Background: Patients with anaplastic thyroid cancer (ATC) have poor overall survival, and the optimal management approach remains unclear. The aim of this study is to evaluate our experience with multimodality (MMT) versus limited treatment (LT) for ATC. Patients and Methods: A cohort study of patients with ATC managed in a tertiary referral center was undertaken. The outcomes of MMT were compared with those of LT. The primary outcome measures were locoregional control and progression-free and overall survival. Secondary outcome measures were treatment-related complications and factors associated with improved survival. Results: In total, 59 patients (35 females) with a median age of 73 years (range 39-99 years) and ATC stage IVA (n = 2), IVB (n = 28), or IVC (n = 29) were included. LT was utilized in 25 patients (42%), and 34 cases had MMT. MMT patients had a longer time of locoregional control (18.5 versus 1.9 months; p < 0.001), progression-free survival (3.5 versus 1.2 months; p < 0.001), and overall survival (6.9 versus 2.0 months; p < 0.001) when compared with LT. For patients with stage IVC ATC, locoregional control (p = 0.03), progression-free survival (p < 0.001), and overall survival (p < 0.001) were superior in the MMT cohort compared with LT. MMT had more treatment-related complications than LT (p < 0.001). An Eastern Cooperative Oncology Group performance status < 2 (HR 0.30; p = 0.001) and MMT (HR 0.35; p = 0.008) were associated with improved overall survival. Conclusion: MMT is likely to improve locoregional control, progression-free survival, and overall survival in selected ATC patients including stage IVC tumors but comes with a greater complication risk

Dynamical Patterns of Cattle Trade Movements

Despite their importance for the spread of zoonotic diseases, our understanding of the dynamical aspects characterizing the movements of farmed animal populations remains limited as these systems are traditionally studied as static objects and through simplified approximations. By leveraging on the network science approach, here we are able for the first time to fully analyze the longitudinal dataset of Italian cattle movements that reports the mobility of individual animals among farms on a daily basis. The complexity and inter-relations between topology, function and dynamical nature of the system are characterized at different spatial and time resolutions, in order to uncover patterns and vulnerabilities fundamental for the definition of targeted prevention and control measures for zoonotic diseases. Results show how the stationarity of statistical distributions coexists with a strong and non-trivial evolutionary dynamics at the node and link levels, on all timescales. Traditional static views of the displacement network hide important patterns of structural changes affecting nodes' centrality and farms' spreading potential, thus limiting the efficiency of interventions based on partial longitudinal information. By fully taking into account the longitudinal dimension, we propose a novel definition of dynamical motifs that is able to uncover the presence of a temporal arrow describing the evolution of the system and the causality patterns of its displacements, shedding light on mechanisms that may play a crucial role in the definition of preventive actions

Dynamical Patterns of Cattle Trade Movements

Despite their importance for the spread of zoonotic diseases, our understanding of the dynamical aspects characterizing the movements of farmed animal populations remains limited as these systems are traditionally studied as static objects and through simplified approximations. By leveraging on the network science approach, here we are able for the first time to fully analyze the longitudinal dataset of Italian cattle movements that reports the mobility of individual animals among farms on a daily basis. The complexity and inter-relations between topology, function and dynamical nature of the system are characterized at different spatial and time resolutions, in order to uncover patterns and vulnerabilities fundamental for the definition of targeted prevention and control measures for zoonotic diseases. Results show how the stationarity of statistical distributions coexists with a strong and non-trivial evolutionary dynamics at the node and link levels, on all timescales. Traditional static views of the displacement network hide important patterns of structural changes affecting nodes' centrality and farms' spreading potential, thus limiting the efficiency of interventions based on partial longitudinal information. By fully taking into account the longitudinal dimension, we propose a novel definition of dynamical motifs that is able to uncover the presence of a temporal arrow describing the evolution of the system and the causality patterns of its displacements, shedding light on mechanisms that may play a crucial role in the definition of preventive actions