Intersections of homogeneous Cantor sets and beta-expansions

Let $\Gamma_{\beta,N}$ be the $N$-part homogeneous Cantor set with $\beta\in(1/(2N-1),1/N)$. Any string $(j_\ell)_{\ell=1}^\N$ with $j_\ell\in\{0,\pm 1,...,\pm(N-1)\}$ such that $t=\sum_{\ell=1}^\N j_\ell\beta^{\ell-1}(1-\beta)/(N-1)$ is called a code of $t$. Let $\mathcal{U}_{\beta,\pm N}$ be the set of $t\in[-1,1]$ having a unique code, and let $\mathcal{S}_{\beta,\pm N}$ be the set of $t\in\mathcal{U}_{\beta,\pm N}$ which make the intersection $\Gamma_{\beta,N}\cap(\Gamma_{\beta,N}+t)$ a self-similar set. We characterize the set $\mathcal{U}_{\beta,\pm N}$ in a geometrical and algebraical way, and give a sufficient and necessary condition for $t\in\mathcal{S}_{\beta,\pm N}$. Using techniques from beta-expansions, we show that there is a critical point $\beta_c\in(1/(2N-1),1/N)$, which is a transcendental number, such that $\mathcal{U}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\beta_c)$, and contains countably infinite many elements if $\beta\in(\beta_c,1/N)$. Moreover, there exists a second critical point $\alpha_c=\big[N+1-\sqrt{(N-1)(N+3)}\,\big]/2\in(1/(2N-1),\beta_c)$ such that $\mathcal{S}_{\beta,\pm N}$ has positive Hausdorff dimension if $\beta\in(1/(2N-1),\alpha_c)$, and contains countably infinite many elements if $\beta\in[\alpha_c,1/N)$.Comment: 23 pages, 4 figure

Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality

We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al, Nature Physics 2012], we show that any combination of local common causes and direct causes satisfying this principle, i.e. propagating at any finite speed, leads to signalling. This is true even if the common and direct causes are allowed to propagate at a supraluminal-but-finite speed defined in a Newtonian-like privileged universal reference frame. Consequently, either there is supraluminal communication or the conclusion that Nature is nonlocal (i.e. discontinuous) is unavoidable.Comment: It is an honor to dedicate this article to Yakir Aharonov, the master of quantum paradoxes. Version 2 contains some more references and a clarified conclusio

Marine latitude/altitude OH distributions: Comparison of Pacific Ocean observations with models

Reported here are tropical/subtropical Pacific basin OH observational data presented in a latitude/altitude geographical grid. They cover two seasons of the year (spring and fall) that reflect the timing of NASA's PEM-Tropics A (1996) and B (1999) field programs. Two different OH sensors were used to collect these data, and each instrument was mounted on a different aircraft platform (i.e., NASA's P-3B and DC-8). Collectively, these chemical snapshots of the central Pacific have revealed several interesting trends. Only modest decreases (factors of 2 to 3) were found in the levels of OH with increasing altitude (0-12 km). Similarly, only modest variations were found (factors of 1.5 to 3.5) when the data were examined as a function of latitude (30° N to 30° S). Using simultaneously recorded data for CO, O3, H2O, NO, and NMHCs, comparisons with current models were also carried out. For three out of four data subsets, the results revealed a high level of correspondence. On average, the box model results agreed with the observations within a factor of 1.5. The comparison with the three-dimensional model results was found to be only slightly worse. Overall, these results suggest that current model mechanisms capture the major photochemical processes controlling OH quite well and thus provide a reasonably good representation of OH levels for tropical marine environments. They also indicate that the two OH sensors employed during the PEM-Tropics B study generally saw similar OH levels when sampling a similar tropical marine environment. However, a modest altitude bias appears to exist between these instruments. More rigorous instrument intercomparison activity would therefore seem to be justified. Further comparisons of model predictions with observations are also recommended for nontropical marine environments as well as those involving highly elevated levels of reactive non-methane hydrocarbons. Copyright 2001 by the American Geophysical Union

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained

Structure and Dynamics of the G121V Dihydrofolate Reductase Mutant: Lessons from a Transition-State Inhibitor Complex

It is well known that enzyme flexibility is critical for function. This is due to the observation that the rates of intramolecular enzyme motions are often matched to the rates of intermolecular events such as substrate binding and product release. Beyond this role in progression through the reaction cycle, it has been suggested that enzyme dynamics may also promote the chemical step itself. Dihydrofolate reductase (DHFR) is a model enzyme for which dynamics have been proposed to aid in both substrate flux and catalysis. The G121V mutant of DHFR is a well studied form that exhibits a severe reduction in the rate of hydride transfer yet there remains dispute as to whether this defect is caused by altered structure, dynamics, or both. Here we address this by presenting an NMR study of the G121V mutant bound to reduced cofactor and the transition state inhibitor, methotrexate. NMR chemical shift markers demonstrate that this form predominantly adopts the closed conformation thereby allowing us to provide the first glimpse into the dynamics of a catalytically relevant complex. Based on 15N and 2H NMR spin relaxation, we find that the mutant complex has modest changes in ps-ns flexibility with most affected residues residing in the distal adenosine binding domain rather than the active site. Thus, aberrant ps-ns dynamics are likely not the main contributor to the decreased catalytic rate. The most dramatic effect of the mutation involves changes in µs-ms dynamics of the F-G and Met20 loops. Whereas loop motion is quenched in the wild type transition state inhibitor complex, the F-G and Met20 loops undergo excursions from the closed conformation in the mutant complex. These excursions serve to decrease the population of conformers having the correct active site configuration, thus providing an explanation for the G121V catalytic defect

Holder exponents of irregular signals and local fractional derivatives

It has been recognized recently that fractional calculus is useful for handling scaling structures and processes. We begin this survey by pointing out the relevance of the subject to physical situations. Then the essential definitions and formulae from fractional calculus are summarized and their immediate use in the study of scaling in physical systems is given. This is followed by a brief summary of classical results. The main theme of the review rests on the notion of local fractional derivatives. There is a direct connection between local fractional differentiability properties and the dimensions/ local Holder exponents of nowhere differentiable functions. It is argued that local fractional derivatives provide a powerful tool to analyse the pointwise behaviour of irregular signals and functions.Comment: 20 pages, Late

Clinical Manifestations of an Outbreak of Monkeypox Virus in Captive Chimpanzees in Cameroon, 2016

Monkeypox virus (MPXV) is a re-emerging virus of global concern. An outbreak of Clade I MPXV affected 20 captive chimpanzees in Cameroon in 2016. We describe the epidemiology, virology, phylogenetics, and clinical progression of this outbreak. Clinical signs included exanthema, facial swelling, peri-laryngeal swelling, and eschar. Mpox can be lethal in captive chimpanzees with death likely resulting from respiratory complications. We advise avoiding anesthesia in animals with respiratory signs to reduce the likelihood of death. This outbreak presented a risk to animal care staff. There is a need for increased awareness and a One Health approach to preparation for outbreaks in wildlife rescue centers in primate range states where MPXV occurs. Control measures should include quarantining affected animals, limiting human contacts, surveillance of humans and animals, use of personal protective equipment, and regular decontamination of enclosures.</p

Steady state free radical budgets and ozone photochemistry during TOPSE

A steady state model, constrained by a number of measured quantities, was used to derive peroxy radical levels for the conditions of the Tropospheric Ozone Production about the Spring Equinox (TOPSE) campaign. The analysis is made using data collected aboard the NCAR/NSF C‐130 aircraft from February through May 2000 at latitudes from 40° to 85°N, and at altitudes from the surface to 7.6 km. HO2 + RO2 radical concentrations were measured during the experiment, which are compared with model results over the domain of the study showing good agreement on the average. Average measurement/model ratios are 1.04 (σ = 0.73) and 0.96 (σ = 0.52) for the MLB and HLB, respectively. Budgets of total peroxy radical levels as well as of individual free radical members were constructed, which reveal interesting differences compared to studies at lower latitudes. The midlatitude part of the study region is a significant net source of ozone, while the high latitudes constitute a small net sink leading to the hypothesis that transport from the middle latitudes can explain the observed increase in ozone in the high latitudes. Radical reservoir species concentrations are modeled and compared with the observations. For most conditions, the model does a good job of reproducing the formaldehyde observations, but the peroxide observations are significantly less than steady state for this study. Photostationary state (PSS) derived total peroxy radical levels and NO/NO2 ratios are compared with the measurements and the model; PSS‐derived results are higher than observations or the steady state model at low NO concentrations