39 research outputs found
On level line fluctuations of SOS surfaces above a wall
We study the low temperature D Solid-On-Solid model on
with zero boundary conditions and non-negative heights (a floor at height ).
Caputo et al. (2016) established that this random surface typically admits
either or many nested macroscopic level line
loops for an explicit ,
and its top loop has cube-root fluctuations: e.g., if
is the vertical displacement of from the bottom boundary point
, then over . It is believed that rescaling by
and by would yield a limit law of a diffusion on
. However, no nontrivial lower bound was known on for a fixed
(e.g., ), let alone on in , to
complement the bound on . Here we show a lower bound of the
predicted order : for every there exists such
that with probability at least
. The proof relies on the Ornstein--Zernike machinery due to
Campanino--Ioffe--Velenik, and a result of Ioffe, Shlosman and Toninelli (2015)
that rules out pinning in Ising polymers with modified interactions along the
boundary. En route, we refine the latter result into a Brownian excursion limit
law, which may be of independent interest.Comment: 48 pages, 2 figure
Trace Formulae and Spectral Statistics for Discrete Laplacians on Regular Graphs (I)
Trace formulae for d-regular graphs are derived and used to express the
spectral density in terms of the periodic walks on the graphs under
consideration. The trace formulae depend on a parameter w which can be tuned
continuously to assign different weights to different periodic orbit
contributions. At the special value w=1, the only periodic orbits which
contribute are the non back- scattering orbits, and the smooth part in the
trace formula coincides with the Kesten-McKay expression. As w deviates from
unity, non vanishing weights are assigned to the periodic walks with
back-scatter, and the smooth part is modified in a consistent way. The trace
formulae presented here are the tools to be used in the second paper in this
sequence, for showing the connection between the spectral properties of
d-regular graphs and the theory of random matrices.Comment: 22 pages, 3 figure
Lower Bounds on the Time/Memory Tradeoff of Function Inversion
We study time/memory tradeoffs of function inversion: an algorithm, i.e., an inverter, equipped with an -bit advice on a randomly chosen function and using oracle queries to , tries to invert a randomly chosen output of , i.e., to find . Much progress was done regarding adaptive function inversion - the inverter is allowed to make adaptive oracle queries. Hellman [IEEE transactions on Information Theory \u2780] presented an adaptive inverter that inverts with high probability a random . Fiat and Naor [SICOMP \u2700] proved that for any with (ignoring low-order terms), an -advice, -query variant of Hellman\u27s algorithm inverts a constant fraction of the image points of any function. Yao [STOC \u2790] proved a lower bound of for this problem. Closing the gap between the above lower and upper bounds is a long-standing open question.
Very little is known for the non-adaptive variant of the question - the inverter chooses its queries in advance. The only known upper bounds, i.e., inverters, are the trivial ones (with ), and the only lower bound is the above bound of Yao. In a recent work, Corrigan-Gibbs and Kogan [TCC \u2719] partially justified the difficulty of finding lower bounds on non-adaptive inverters, showing that a lower bound on the time/memory tradeoff of non-adaptive inverters implies a lower bound on low-depth Boolean circuits. Bounds that, for a strong enough choice of parameters, are notoriously hard to prove.
We make progress on the above intriguing question, both for the adaptive and the non-adaptive case, proving the following lower bounds on restricted families of inverters:
- Linear-advice (adaptive inverter): If the advice string is a linear function of (e.g., , for some matrix , viewing as a vector in ), then . The bound generalizes to the case where the advice string of , i.e., the coordinate-wise addition of the truth tables of and , can be computed from the description of and by a low communication protocol.
- Affine non-adaptive decoders: If the non-adaptive inverter has an affine decoder - it outputs a linear function, determined by the advice string and the element to invert, of the query answers - then (regardless of ).
- Affine non-adaptive decision trees: If the non-adaptive inversion algorithm is a -depth affine decision tree - it outputs the evaluation of a decision tree whose nodes compute a linear function of the answers to the queries - and , then
Glauber Dynamics for the mean-field Potts Model
We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with
states and show that it undergoes a critical slowdown at an
inverse-temperature strictly lower than the critical
for uniqueness of the thermodynamic limit. The dynamical critical
is the spinodal point marking the onset of metastability.
We prove that when the mixing time is asymptotically
and the dynamics exhibits the cutoff phenomena, a sharp
transition in mixing, with a window of order . At the
dynamics no longer exhibits cutoff and its mixing obeys a power-law of order
. For the mixing time is exponentially large in
. Furthermore, as with , the mixing time
interpolates smoothly from subcritical to critical behavior, with the latter
reached at a scaling window of around . These results
form the first complete analysis of mixing around the critical dynamical
temperature --- including the critical power law --- for a model with a first
order phase transition.Comment: 45 pages, 5 figure
The ProPrems trial: investigating the effects of probiotics on late onset sepsis in very preterm infants
BACKGROUND: Late onset sepsis is a frequent complication of prematurity associated with increased mortality and morbidity. The commensal bacteria of the gastrointestinal tract play a key role in the development of healthy immune responses. Healthy term infants acquire these commensal organisms rapidly after birth. However, colonisation in preterm infants is adversely affected by delivery mode, antibiotic treatment and the intensive care environment. Altered microbiota composition may lead to increased colonisation with pathogenic bacteria, poor immune development and susceptibility to sepsis in the preterm infant.Probiotics are live microorganisms, which when administered in adequate amounts confer health benefits on the host. Amongst numerous bacteriocidal and nutritional roles, they may also favourably modulate host immune responses in local and remote tissues. Meta-analyses of probiotic supplementation in preterm infants report a reduction in mortality and necrotising enterocolitis. Studies with sepsis as an outcome have reported mixed results to date.Allergic diseases are increasing in incidence in "westernised" countries. There is evidence that probiotics may reduce the incidence of these diseases by altering the intestinal microbiota to influence immune function. METHODS/DESIGN: This is a multi-centre, randomised, double blinded, placebo controlled trial investigating supplementing preterm infants born at < 32 weeks' gestation weighing < 1500 g, with a probiotic combination (Bifidobacterium infantis, Streptococcus thermophilus and Bifidobacterium lactis). A total of 1,100 subjects are being recruited in Australia and New Zealand. Infants commence the allocated intervention from soon after the start of feeds until discharge home or term corrected age. The primary outcome is the incidence of at least one episode of definite (blood culture positive) late onset sepsis before 40 weeks corrected age or discharge home. Secondary outcomes include: Necrotising enterocolitis, mortality, antibiotic usage, time to establish full enteral feeds, duration of hospital stay, growth measurements at 6 and 12 months' corrected age and evidence of atopic conditions at 12 months' corrected age. DISCUSSION: Results from previous studies on the use of probiotics to prevent diseases in preterm infants are promising. However, a large clinical trial is required to address outstanding issues regarding safety and efficacy in this vulnerable population. This study will address these important issues. TRIAL REGISTRATION: Australia and New Zealand Clinical Trials Register (ANZCTR): ACTRN012607000144415The product "ABC Dophilus Probiotic Powder for InfantsÂź", Solgar, USA has its 3 probiotics strains registered with the Deutsche Sammlung von Mikroorganismen und Zellkulturen (DSMZ--German Collection of Microorganisms and Cell Cultures) as BB-12 15954, B-02 96579, Th-4 15957
The Scholar and the Future of the Research Library (Book Rerview)
published or submitted for publicatio
The maximum of branching Brownian motion in
We show that in branching Brownian motion (BBM) in , ,
the law of , the maximum distance of a particle from the origin at time
, converges as to the law of a randomly shifted Gumbel random
variable.Comment: 53 pages, 7 figures. Revision addresses referees comments and refers
to the recent arXiv:2112.08407. To appear in the Annals of Applied
Probabilit
A computational gene expression score for predicing immune injury in renal allografts
Background Whole genome microarray meta-analyses of 1030 kidney, heart, lung and liver allograft biopsies identified a common immune response module (CRM) of 11 genes that define acute rejection (AR) across different engrafted tissues. We evaluated if the CRM genes can provide a molecular microscope to quantify graft injury in acute rejection (AR) and predict risk of progressive interstitial fibrosis and tubular atrophy (IFTA) in histologically normal kidney biopsies. Methods Computational modeling was done on tissue qPCR based gene expression measurements for the 11 CRM genes in 146 independent renal allografts from 122 unique patients with AR (n = 54) and no-AR (n = 92). 24 demographically matched patients with no-AR had 6 and 24 month paired protocol biopsies; all had histologically normal 6 month biopsies, and 12 had evidence of progressive IFTA (pIFTA) on their 24 month biopsies. Results were correlated with demographic, clinical and pathology variables. Results The 11 gene qPCR based tissue CRM score (tCRM) was significantly increased in AR (5.68 ± 0.91) when compared to STA (1.29 ± 0.28; p < 0.001) and pIFTA (7.94 ± 2.278 versus 2.28 ± 0.66; p = 0.04), with greatest significance for CXCL9 and CXCL10 in AR (p <0.001) and CD6 (p<0.01), CXCL9 (p<0.05), and LCK (p<0.01) in pIFTA. tCRM was a significant independent correlate of biopsy confirmed AR (p < 0.001; AUC of 0.900; 95% CI = 0.705-903). Gene expression modeling of 6 month biopsies across 7/11 genes (CD6, INPP5D, ISG20, NKG7, PSMB9, RUNX3, and TAP1) significantly (p = 0.037) predicted the development of pIFTA at 24 months. Conclusions Genome-wide tissue gene expression data mining has supported the development of a tCRM-qPCR based assay for evaluating graft immune inflammation. The tCRM score quantifies injury in AR and stratifies patients at increased risk of future pIFTA prior to any perturbation of graft function or histology