Proof of Single-Replica Equivalence in Short-Range Spin Glasses.

We consider short-range Ising spin glasses in equilibrium at infinite system size, and prove that, for fixed bond realization and a given Gibbs state drawn from a suitable metastate, each translation and locally invariant function (for example, self-overlaps) of a single pure state in the decomposition of the Gibbs state takes the same value for all the pure states in that Gibbs state. We describe several significant applications to spin glasses.

Complexity as information in spin-glass Gibbs states and metastates: Upper bounds at nonzero temperature and long-range models.

In classical finite-range spin systems, especially those with disorder such as spin glasses, a low-temperature Gibbs state may be a mixture of a number of pure or ordered states; the complexity of the Gibbs state has been defined in the past roughly as the logarithm of this number, assuming the question is meaningful in a finite system. As nontrivial pure-state structure is lost in finite size, in a recent paper [Phys. Rev. E 101, 042114 (2020)2470-004510.1103/PhysRevE.101.042114] Höller and the author introduced a definition of the complexity of an infinite-size Gibbs state as the mutual information between the pure state and the spin configuration in a finite region, and applied this also within a metastate construction. (A metastate is a probability distribution on Gibbs states.) They found an upper bound on the complexity for models of Ising spins in which each spin interacts with only a finite number of others, in terms of the surface area of the region, for all T≥0. In the present paper, the complexity of a metastate is defined likewise in terms of the mutual information between the Gibbs state and the spin configuration. Upper bounds are found for each of these complexities for general finite-range (i.e., short- or long-range, in a sense we define) mixed p-spin interactions of discrete or continuous spins (such as m-vector models), but only for T>0. For short-range models, the bound reduces to the surface area. For long-range interactions, the definition of a Gibbs state has to be modified, and for these models we also prove that the states obtained within the metastate constructions are Gibbs states under the modified definition. All results are valid for a large class of disorder distributions.

Nontrivial maturation metastate-average state in a one-dimensional long-range Ising spin glass: Above and below the upper critical range.

Understanding the low-temperature pure state structure of spin glasses remains an open problem in the field of statistical mechanics of disordered systems. Here we study Monte Carlo dynamics, performing simulations of the growth of correlations following a quench from infinite temperature to a temperature well below the spin-glass transition temperature T_{c} for a one-dimensional Ising spin-glass model with diluted long-range interactions. In this model, the probability P_{ij} that an edge {i,j} has nonvanishing interaction falls as a power law with chord distance, P_{ij}∝1/R_{ij}^{2σ}, and we study a range of values of σ with 1/2<σ<1. We consider a correlation function C_{4}(r,t). A dynamic correlation length that shows power-law growth with time ξ(t)∝t^{1/z} can be identified in the data and, for large time t, C_{4}(r,t) decays as a power law r^{-α_{d}} with distance r when r≪ξ(t). The calculation can be interpreted in terms of the maturation metastate averaged Gibbs state, or MMAS, and the decay exponent α_{d} differentiates between a trivial MMAS (α_{d}=0), as expected in the droplet picture of spin glasses, and a nontrivial MMAS (α_{d}≠0), as in the replica-symmetry-breaking (RSB) or chaotic pairs pictures. We find nonzero α_{d} even in the regime σ>2/3 which corresponds to short-range systems below six dimensions. For σ<2/3, the decay exponent α_{d} follows the RSB prediction for the decay exponent α_{s}=3-4σ of the static metastate, consistent with a conjectured statics-dynamics relation, while it approaches α_{d}=1-σ in the regime 2/3<σ<1; however, it deviates from both lines in the vicinity of σ=2/3.

Delay in diagnosis of patients with head-and-neck cancer in Canada: impact of patient and provider delay.

Background: Head-and-neck cancers (hncs) often present at an advanced stage, leading to poor outcomes. Late presentation might be attributable to patient delays (reluctance to seek treatment, for instance) or provider delays (misdiagnosis, prolonged wait time for consultation, for example). The objective of the present study was to examine the length and cause of such delays in a Canadian universal health care setting. Methods: Patients presenting for the first time to the hnc multidisciplinary team (mdt) with a biopsy-proven hnc were recruited to this study. Patients completed a survey querying initial symptom presentation, their previous medical appointments, and length of time between appointments. Clinical and demographic data were collected for all patients. Results: The average time for patients to have their first appointment at the mdt clinic was 15.1 months, consisting of 3.9 months for patients to see a health care provider (hcp) for the first time since symptom onset and 10.7 months from first hcp appointment to the mdt clinic. Patients saw an average of 3 hcps before the mdt clinic visit (range: 1-7). No significant differences in time to presentation were found based on stage at presentation or anatomic site. Conclusions: At our tertiary care cancer centre, a patient's clinical pathway to being seen at the mdt clinic shows significant delays, particularly in the time from the first hcp visit to mdt referral. Possible methods to mitigate delay include education about hnc for patients and providers alike, and a more streamlined referral system.

One-step replica-symmetry-breaking phase below the de Almeida-Thouless line in low-dimensional spin glasses.

The de Almeida-Thouless (AT) line is the phase boundary in the temperature-magnetic field plane of an Ising spin glass at which a continuous (i.e., second-order) transition from a paramagnet to a replica-symmetry-breaking (RSB) phase occurs, according to mean-field theory. Here, using field-theoretic perturbative renormalization group methods on the Bray-Roberts reduced Landau-Ginzburg-type theory for a short-range Ising spin glass in space of dimension d, we show that at nonzero magnetic field the nature of the corresponding transition is modified as follows: (a) For d-6 small and positive, with increasing field on the AT line, first, the ordered phase just below the transition becomes the so-called one-step RSB, instead of the full RSB that occurs in mean-field theory; the transition on the AT line remains continuous with a diverging correlation length. Then at a higher field, a tricritical point separates the latter transition from a quasi-first-order one, that is one at which the correlation length does not diverge, and there is a jump in part of the order parameter, but no latent heat. The location of the tricritical point tends to zero as d→6^{+}. (b) For d≤6, we argue that the quasi-first-order transition could persist down to arbitrarily small nonzero fields, with a transition to full RSB still expected at lower temperature. Whenever the quasi-first-order transition occurs, it is at a higher temperature than the AT transition would be for the same field, preempting it as the temperature is lowered. These results may explain the reported absence of a diverging correlation length in the presence of a magnetic field in low-dimensional spin glasses in some simulations and in high-temperature series expansions. We also draw attention to the similarity of the "dynamically frozen" state, which occurs at temperatures just above the quasi-first-order transition, and the "metastate-average state" of the one-step RSB phase, and discuss the issue of the number of pure states in either.

Multicritical Point on the de Almeida-Thouless Line in Spin Glasses in d>6 Dimensions.

The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature T and magnetic field h plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that, when the dimension d of space is just above six, there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime, where the RG flows run away to infinite coupling strength; as d approaches six from above, the MCP approaches the zero-field critical point exponentially in 1/(d-6). Thus, on the AT line, perturbation theory for the critical properties breaks down at a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when d≤6, as was known previously. We calculate the exponents at the MCP to first order in ϵ=d-6>0. The fate of the MCP as d increases from just above six to infinity is not known.

Triviality of the ground-state metastate in long-range Ising spin glasses in one dimension.

We consider the one-dimensional model of a spin glass with independent Gaussian-distributed random interactions, which have mean zero and variance 1/|i-j|^{2σ}, between the spins at sites i and j for all i≠j. It is known that, for σ>1, there is no phase transition at any nonzero temperature in this model. We prove rigorously that, for σ>3/2, any translation-covariant Newman-Stein metastate for the ground states (i.e., the frequencies with which distinct ground states are observed in finite-size samples in the limit of infinite size, for given disorder) is trivial and unique. In other words, for given disorder and asymptotically at large sizes, the same ground state, or its global spin flip, is obtained (almost) always. The proof consists of two parts: One is a theorem (based on one by Newman and Stein for short-range two-dimensional models), valid for all σ>1, that establishes triviality under a convergence hypothesis on something similar to the energies of domain walls and the other (based on older results for the one-dimensional model) establishes that the hypothesis is true for σ>3/2. In addition, we derive heuristic scaling arguments and rigorous exponent inequalities which tend to support the validity of the hypothesis under broader conditions. The constructions of various metastates are extended to all values σ>1/2. Triviality of the metastate in bond-diluted power-law models for σ>1 is proved directly.

Short-range Ising spin glasses: the metastate interpretation of replica symmetry breaking.

Parisi's formal replica-symmetry-breaking (RSB) scheme for mean-field spin glasses has long been interpreted in terms of many pure states organized ultrametrically. However, the early version of this interpretation, as applied to the short-range Edwards-Anderson model, runs into problems because as shown by Newman and Stein (NS) it does not allow for chaotic size dependence, and predicts non-self-averaging that cannot occur. NS proposed the concept of the metastate (a probability distribution over infinite-size Gibbs states in a given sample that captures the effects of chaotic size dependence) and a nonstandard interpretation of the RSB results in which the metastate is nontrivial and is responsible for what was called non-self-averaging. In this picture, each state drawn from the metastate has the ultrametric properties of the old theory, but when the state is averaged using the metastate, the resulting mixed state has little structure. This picture was constructed so as to agree both with the earlier RSB results and with rigorous results. Here we use the effective field theory of RSB, in conjunction with the rigorous definitions of pure states and the metastate in infinite-size systems, to show that the nonstandard picture follows directly from the RSB mean-field theory. In addition, the metastate-averaged state possesses power-law correlations throughout the low-temperature phase; the corresponding exponent ζ takes the value 4 according to the field theory in high dimensions d, and describes the effective fractal dimension of clusters of spins. Further, the logarithm of the number of pure states in the decomposition of the metastate-averaged state that can be distinguished if only correlations in a window of size W can be observed is of order W(d-ζ). These results extend the nonstandard picture quantitatively; we show that arguments against this scenario are inconclusive. More generally, in terms of Parisi's function q(x), if q(0)≠∫(0)(1)dxq(x), then the metastate is nontrivial. In an Appendix, we also prove rigorously that the metastate-averaged state of the Sherrington-Kirkpatrick model is a uniform distribution on all spin configurations at all temperatures.

Paediatric hereditary angioedema: a survey of UK service provision and patient experience.

Hereditary angioedema (HAE) is a rare disease characterized by episodes of potentially life-threatening angioedema. For affected children in the United Kingdom, there are relatively few data regarding disease prevalence, service organization and the humanistic burden of the disease. To improve knowledge in these areas, we surveyed major providers of care for children with HAE. A questionnaire was sent to major paediatric centres to determine patient numbers, symptoms, diagnostic difficulties, management and available services. In addition, all patients at a single centre were given a questionnaire to determine the experiences of children and their families. Sixteen of 28 centres responded, caring for a total of 111 UK children. Seven children had experienced life-threatening crises. One-third of patients were on long-term prophylactic medication, including C1 inhibitor prophylaxis in four children. Eight centres reported patients who were initially misdiagnosed. Broad differences in management were noted, particularly regarding indications for long-term prophylaxis and treatment monitoring. We also noted substantial variation in the organization of services between centres, including the number of consultants contributing to patient care, the availability of specialist nurses, the availability of home therapy training and the provision of patient information. Ten of 12 patient/carer questionnaires were returned, identifying three common themes: the need to access specialist knowledge, the importance of home therapy and concerns around the direct effect of angioedema on their life. To our knowledge, this study represents the first dedicated survey of paediatric HAE services in the United Kingdom and provides useful information to inform the optimization of services.

Phase 1 study of nab-paclitaxel, cisplatin and 5-fluorouracil as induction chemotherapy followed by concurrent chemoradiotherapy in locoregionally advanced squamous cell carcinoma of the oropharynx.

BACKGROUND: Induction chemotherapy followed by concurrent chemoradiation (CRT) (sequential therapy) has been evaluated in the treatment of locoregionally-advanced squamous cell cancer of the head and neck (LA-SCCHN), with docetaxel, cisplatin (P) and 5-flurouracil (F) shown to be superior to PF doublet. Nab-paclitaxel (A) is a novel albumin-bound paclitaxel with a superior therapeutic index to docetaxel. METHODS: A phase I trial [Clinical trials.gov identifier NCT00731380] to assess the safety and efficacy of nab-paclitaxel+cisplatin+5-fluorouracil (APF) as induction chemotherapy for three cycles, followed by concurrent carboplatin (area-under-curve (AUC) 1.5 weekly) with radiation therapy (RT) (70 Gy/35 fractions), was conducted using a 3+3 design in patients with previously untreated LA-SCCHN. Dose-limiting toxicities (DLTs) included: standard haematologic and non-haematologic toxicities, treatment delays, inability to complete ⩾95% of RT and skin/mucosal toxicity related to RT assessed from day 1 of treatment to 8 weeks after completion of CRT. RESULTS: 17 patients with oropharyngeal cancer were enrolled in three dose levels, with 15 patients evaluable for DLT. The median age was 54 years (range, 44-65 years), 14 patients were male, and 11 patients' tumours were p16 positive and four negative. Grade 3/4 adverse events during APF (%total number of cycles) were hyponatraemia (14%) neutropenia (10%), lymphopaenia (4%) and thrombocytopenia (2%) during 49 evaluable APF cycles. Febrile neutropenia occurred during one cycle of treatment. CONCLUSION: The recommended phase 2 dose of APF is nab-paclitaxel 100mg/m(2) days 1 and 8, cisplatin 75 mg/mg(2) day 1 and 5-fluorouracil 1000 mg/m(2)/day×96 h days 1-4, every 3 weeks, for three cycles prior to CRT.

The epidemic of human papillomavirus and oropharyngeal cancer in a Canadian population.

BACKGROUND: Sexually transmitted infection with the human papillomavirus (hpv) is responsible for a significant burden of human cancers involving the cervix, anogenital tract, and oropharynx. Studies in the United States and Europe have demonstrated an alarming increase in the frequency of hpv-positive oropharyngeal cancer, but the same direct evidence does not exist in Canada. METHODS: Using the London Health Sciences Centre pathology database, we identified tonsillar cancers diagnosed between 1993 and 2011. Real-time polymerase chain reaction was then used on pre-treatment primary-site biopsy samples to test for dna from the high-risk hpv types 16 and 18. The study cohort was divided into three time periods: 1993-1999, 2000-2005, and 2006-2011. RESULTS: Of 160 tumour samples identified, 91 (57%) were positive for hpv 16. The total number of tonsillar cancers significantly increased from 1993-1999 to 2006-2011 (32 vs. 68), and the proportion of cases that were hpv-positive substantially increased (25% vs. 62%, p < 0.002). Those changes were associated with a marked improvement in 5-year overall survival (39% in 1993-1999 vs. 84% in 2006-2011, p < 0.001). When all factors were included in a multivariable model, only hpv status predicted treatment outcome. INTERPRETATION: The present study is the first to provide direct evidence that hpv-related oropharyngeal cancer is increasing in incidence in a Canadian population. Given the long lag time between hpv infection and clinically apparent malignancy, oropharyngeal cancer will be a significant clinical problem for the foreseeable future despite vaccination efforts.

Entanglement spectra of complex paired superfluids.

We study the entanglement in various fully gapped complex paired states of fermions in two dimensions, focusing on the entanglement spectrum (ES), and using the Bardeen-Cooper-Schrieffer (BCS) form of the ground-state wave function on a cylinder. Certain forms of the pairing functions allow a simple and explicit exact solution for the ES. In the weak-pairing phase of ℓ-wave paired spinless fermions (ℓ odd), the universal low-lying part of the ES consists of |ℓ| chiral Majorana fermion modes [or 2|ℓ| (ℓ even) for spin-singlet states]. For |ℓ|>1, the pseudoenergies of the modes are split in general, but for all ℓ there is a zero-pseudoenergy mode at a zero wave vector if the number of modes is odd. This ES agrees with the perturbed conformal field theory of the edge excitations. For more general BCS states, we show how the entanglement gap diverges as a model pairing function is approached.

Membrane fluidity determines sensitivity of filamentous fungi to chitosan.

The antifungal mode of action of chitosan has been studied for the last 30 years, but is still little understood. We have found that the plasma membrane forms a barrier to chitosan in chitosan-resistant but not chitosan-sensitive fungi. The plasma membranes of chitosan-sensitive fungi were shown to have more polyunsaturated fatty acids than chitosan-resistant fungi, suggesting that their permeabilization by chitosan may be dependent on membrane fluidity. A fatty acid desaturase mutant of Neurospora crassa with reduced plasma membrane fluidity exhibited increased resistance to chitosan. Steady-state fluorescence anisotropy measurements on artificial membranes showed that chitosan binds to negatively charged phospholipids that alter plasma membrane fluidity and induces membrane permeabilization, which was greatest in membranes containing more polyunsaturated lipids. Phylogenetic analysis of fungi with known sensitivity to chitosan suggests that chitosan resistance may have evolved in nematophagous and entomopathogenic fungi, which naturally encounter chitosan during infection of arthropods and nematodes. Our findings provide a method to predict the sensitivity of a fungus to chitosan based on its plasma membrane composition, and suggests a new strategy for antifungal therapy, which involves treatments that increase plasma membrane fluidity to make fungi more sensitive to fungicides such as chitosan.

Theory of minimum spanning trees. I. Mean-field theory and strongly disordered spin-glass model.

The minimum spanning tree (MST) is a combinatorial optimization problem: given a connected graph with a real weight ("cost") on each edge, find the spanning tree that minimizes the sum of the total cost of the occupied edges. We consider the random MST, in which the edge costs are (quenched) independent random variables. There is a strongly disordered spin-glass model due to Newman and Stein [Phys. Rev. Lett. 72, 2286 (1994)], which maps precisely onto the random MST. We study scaling properties of random MSTs using a relation between Kruskal's greedy algorithm for finding the MST, and bond percolation. We solve the random MST problem on the Bethe lattice (BL) with appropriate wired boundary conditions and calculate the fractal dimension D=6 of the connected components. Viewed as a mean-field theory, the result implies that on a lattice in Euclidean space of dimension d , there are of order W(d-D) large connected components of the random MST inside a window of size W , and that d=d(c)=D=6 is a critical dimension. This differs from the value 8 suggested by Newman and Stein. We also critique the original argument for 8, and provide an improved scaling argument that again yields d(c)=6 . The result implies that the strongly disordered spin-glass model has many ground states for d>6 , and only of order one below six. The results for MSTs also apply on the Poisson-weighted infinite tree, which is a mean-field approach to the continuum model of MSTs in Euclidean space, and is a limit of the BL. In a companion paper we develop an epsilon=6-d expansion for the random MST on critical percolation clusters.

Theory of minimum spanning trees. II. Exact graphical methods and perturbation expansion at the percolation threshold.

Continuing the program begun by the authors in a previous paper, we develop an exact low-density expansion for the random minimum spanning tree (MST) on a finite graph and use it to develop a continuum perturbation expansion for the MST on critical percolation clusters in space dimension d . The perturbation expansion is proved to be renormalizable in d=6 dimensions. We consider the fractal dimension D(p) of paths on the latter MST; our previous results lead us to predict that D(p)=2 for d>d(c)=6 . Using a renormalization-group approach, we confirm the result for d>6 and calculate D(p) to first order in epsilon=6-d for d<6 using the connection with critical percolation, with the result D(p)=2-epsilon/7+O(epsilon(2)) .

Algorithms for the automated analysis of cellular dynamics within living fungal colonies.

We present robust and efficient algorithms to automate the measurement of nuclear movement and germ tube extension rates in living fungal networks. The aim is to facilitate the understanding of the dynamics and regulation of nuclear migration in growing fungal colonies. The proposed methodology combines a cascade correlation filter to identify nuclear centers from which 2D nuclear velocities are determined and a level set algorithm for centerline extraction to monitor spore (conidial) germling growth. We show how the proposed cascaded filter improves spatial resolution in the presence of noise and is robust when fluorescently labeled nuclei with different intensities are in close proximity to each other. The performance of the filter is evaluated by simulation in comparison to the well known Rayleigh and Sparrow criteria, and experimental evidence is given from clusters of nuclei and nuclei undergoing mitotic division. The capabilities developed have enabled the robust and objective analysis of 10's of Gigabytes of image data that is being exploited by biological scientists.

Chitosan permeabilizes the plasma membrane and kills cells of Neurospora crassa in an energy dependent manner.

Chitosan has been reported to inhibit spore germination and mycelial growth in plant pathogens, but its mode of antifungal action is poorly understood. Following chitosan treatment, we characterized plasma membrane permeabilization, and cell death and lysis in the experimental model, Neurospora crassa. Rhodamine-labeled chitosan was used to show that chitosan is internalized by fungal cells. Cell viability stains and the calcium reporter, aequorin, were used to monitor plasma membrane permeabilization and cell death. Chitosan permeabilization of the fungal plasma membrane and its uptake into fungal cells was found to be energy dependent but not to involve endocytosis. Different cell types (conidia, germ tubes and vegetative hyphae) exhibited differential sensitivity to chitosan with ungerminated conidia being the most sensitive.

Model of hyphal tip growth involving microtubule-based transport.

We propose a simple model for mass transport within a fungal hypha and its subsequent growth. Inspired by the role of microtubule-transported vesicles, we embody the internal dynamics of mass inside a hypha with mutually excluding particles progressing stochastically along a growing one-dimensional lattice. The connection between long-range transport of materials for growth and the resulting extension of the hyphal tip has not previously been addressed in the modeling literature to our knowledge. We derive and analyze mean-field equations for the model and present a phase diagram of its steady-state behavior, which we compare to simulations. We discuss our results in the context of the filamentous fungus Neurospora crassa.

Time-Multiplexed Laguerre-Gaussian holographic optical tweezers for biological applications.

A ferroelectric liquid crystal spatial light modulator is used to generate up to 24 independently controllable traps in a holographic optical tweezers system using time-multiplexed Fresnel zone plates. For use in biological applications, helical zone plates are used to generate Laguerre-Gaussian laser modes. The high speed switching of the ferroelectric device together with recent advances in computer technology enable fast, smooth movement of traps that can be independently controlled in real time. This is demonstrated by the trapping and manipulation of yeast cells and fungal spores.