Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.Comment: 19 page

Why Are Alkali Halide Solid Surfaces Not Wetted By Their Own Melt?

Alkali halide (100) crystal surfaces are anomalous, being very poorly wetted by their own melt at the triple point. We present extensive simulations for NaCl, followed by calculations of the solid-vapor, solid-liquid, and liquid-vapor free energies showing that solid NaCl(100) is a nonmelting surface, and that its full behavior can quantitatively be accounted for within a simple Born-Meyer-Huggins-Fumi-Tosi model potential. The incomplete wetting is traced to the conspiracy of three factors: surface anharmonicities stabilizing the solid surface; a large density jump causing bad liquid-solid adhesion; incipient NaCl molecular correlations destabilizing the liquid surface. The latter is pursued in detail, and it is shown that surface short-range charge order acts to raise the surface tension because incipient NaCl molecular formation anomalously reduces the surface entropy of liquid NaCl much below that of solid NaCl(100).Comment: 4 pages, 3 figure

Total Lymphocyte Count as a Nutritional Parameter in Hospitalized Patients

Background: Nowadays, there are still many malnourished patients during hospitalization, which comprises around 45-50% patients. Malnutrition is related to increased mortality and morbidity rate; therefore, nutritional state should be assessed in hospitalized patients. Total lymphocyte count (TLC) is related to decreased body function in malnutrition and it is a means of nutritional assessment. Until now, there is no data showing association between malnutrition and TLC in hospitalized patients in Indonesia. The objective of this study was to identify the association between malnutrition and TLC &lt; 1,200 cell/mm3 in hospitalized patients. Method: This study was a cross-sectional study. Subjects were new patients hospitalized at internal medicine ward of Cipto Mangunkusumo Hospital. Patients were collected by consecutive sampling. We conducted the study between April and May 2008. Fifty four patients were assessed for malnutrition by the subjective global assessment (SGA) and they also had undergone complete blood count. TLC was numbered with routine complete blood count test. Patients were classified into malnutrition according to SGA. TLC was classified with cut-off point of 1,200 cell/mm3. Statistical analysis included Chi-square test, which was used to compare proportion. Results: There were 52% malnourished patients, 33% patients with TLC &lt; 1,200 cell/mm3, 57% patients with malnutrition and TLC &lt; 1,200 cell/mm3. This study showed that there was an association between malnutrition and TLC &lt; 1,200 cell/mm3 (p = 0.001). Moreover, there was also significant association between severe malnutrition (SGA C) with TLC &lt; 900 cell/mm3 (p = 0.02). Conclusion: There is an association between malnutrition and TLC &lt; 1,200 cell/mm3

Charging Induced Emission of Neutral Atoms from NaCl Nanocube Corners

Detachment of neutral cations/anions from solid alkali halides can in principle be provoked by donating/subtracting electrons to the surface of alkali halide crystals, but generally constitutes a very endothermic process. However, the amount of energy required for emission is smaller for atoms located in less favorable positions, such as surface steps and kinks. For a corner ion in an alkali halide cube the binding is the weakest, so it should be easier to remove that atom, once it is neutralized. We carried out first principles density functional calculations and simulations of neutral and charged NaCl nanocubes, to establish the energetics of extraction of neutralized corner ions. Following hole donation (electron removal) we find that detachment of neutral Cl corner atoms will require a limited energy of about 0.8 eV. Conversely, following the donation of an excess electron to the cube, a neutral Na atom is extractable from the corner at the lower cost of about 0.6 eV. Since the cube electron affinity level (close to that a NaCl(100) surface state, which we also determine) is estimated to lie about 1.8 eV below vacuum, the overall energy balance upon donation to the nanocube of a zero energy electron from vacuum will be exothermic. The atomic and electronic structure of the NaCl(100) surface, and of the nanocube Na and Cl corner vacancies are obtained and analyzed as a byproduct.Comment: 16 pages, 2 table, 7 figure

On the linear independence of spikes and sines

The purpose of this work is to survey what is known about the linear independence of spikes and sines. The paper provides new results for the case where the locations of the spikes and the frequencies of the sines are chosen at random. This problem is equivalent to studying the spectral norm of a random submatrix drawn from the discrete Fourier transform matrix. The proof involves depends on an extrapolation argument of Bourgain and Tzafriri.Comment: 16 pages, 4 figures. Revision with new proof of major theorem

Analisis Pembaharuan Kurikulum Darurat pada Mata Pelajaran Pendidikan Pancasila dan Kewarganegaraan

Kurikulum darurat yang diberlakukan Pemerintah pada masa Pandemi Covid-19 belum efektif dalam membentuk karakter siswa Pendidikan Dasar khususnya melalui Pendidikan Pancasila dan Kewarganegaraan. Tujuan penelitian ini untuk mengetahui permasalahan dan memberikan solusi pada permasalahan pembaharuan kurikulum Pendidikan Pancasila dan Kewarganegaraan. Penelitian ini menggunakan metode penelitian deskriptif dengan pendekatan kualitatif. Lokasi penelitian ini terletak pada SD Katolik Cor Jesu Malang. Hasil penelitian dapat menunjukkan beberapa hal dari permasalahan-permasalahan yang timbul di SD Katolik Cor Jesu Malang tentang pembaharuan kurikulum darurat, seperti guru yang kesulitan dalam menentukan indikator pencapaian hasil belajar, menentukan metode pembelajaran saat online, etika peserta didik dalam proses pembelajaran, kurangnya jam perwalian dalam penyelesaian permasalahan peserta didik secara individu dan para guru masih terbatas dalam hal informasi dan teknologi. Maka dari itu diperlukan inovasi dan penguatan kompetensi guru dalam melaksanakan kurikulum darurat pada Pendidikan Pancasila dan Kewarganegaraan

On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Kick stability in groups and dynamical systems

We consider a general construction of ``kicked systems''. Let G be a group of measure preserving transformations of a probability space. Given its one-parameter/cyclic subgroup (the flow), and any sequence of elements (the kicks) we define the kicked dynamics on the space by alternately flowing with given period, then applying a kick. Our main finding is the following stability phenomenon: the kicked system often inherits recurrence properties of the original flow. We present three main examples. 1) G is the torus. We show that for generic linear flows, and any sequence of kicks, the trajectories of the kicked system are uniformly distributed for almost all periods. 2) G is a discrete subgroup of PSL(2,R) acting on the unit tangent bundle of a Riemann surface. The flow is generated by a single element of G, and we take any bounded sequence of elements of G as our kicks. We prove that the kicked system is mixing for all sufficiently large periods if and only if the generator is of infinite order and is not conjugate to its inverse in G. 3) G is the group of Hamiltonian diffeomorphisms of a closed symplectic manifold. We assume that the flow is rapidly growing in the sense of Hofer's norm, and the kicks are bounded. We prove that for a positive proportion of the periods the kicked system inherits a kind of energy conservation law and is thus superrecurrent. We use tools of geometric group theory and symplectic topology.Comment: Latex, 40 pages, revised versio

Spinless Matter in Transposed-Equi-Affine Theory of Gravity

We derive and discus the equations of motion for spinless matter: relativistic spinless scalar fields, particles and fluids in the recently proposed by A. Saa model of gravity with covariantly constant volume with respect to the transposed connection in Einstein-Cartan spaces. A new interpretation of this theory as a theory with variable Plank "constant" is suggested. We show that the consistency of the semiclassical limit of the wave equation and classical motion dictates a new definite universal interaction of torsion with massive fields.Comment: 29 pages, latex, no figures. New Section on semiclassical limit of wave equation added; old references rearranged; new references, remarks, comments, and acknowledgments added; typos correcte

The role of timely diagnosis and treatment of ENT pathologies in maintaining the physical health of patients

The presented work analyzes the need for specialized diagnostic procedures in order to identify the presence of certain ENT pathologies in the patient, since their untimely detection and, as a result, treatment directly affect the physical health of a person as a whole. It is noted that a decrease in patients’ attention to their health, as well as an untimely appeal to a specialized specialist for advice, can lead to the development of serious complications and even surgical intervention. The authors investigate in detail the features of common ENT diseases, possible symptoms, as well as complications that arise in the case of a chronic course of such diseases. At the same time, considerable emphasis is placed on the importance of the prevention of ENT diseases, among these measures are proper nutrition, a healthy lifestyle, regular medical examinations and following recommendations for the care of ENT organs. The paper emphasizes that timely diagnosis and treatment of ENT pathologies should be identified as key factors that ensure the necessary level of physical health of patients, for this reason, it is necessary to consult a specialist at the first symptoms of the disease. Investigating the methods of diagnosis of ENT diseases, the authors of the work also pay attention to the consideration of methods of treatment of ENT diseases, especially noting conservative therapy, since at the early stages of the development of the disease it allows to restore the patient’s health without resorting to surgical intervention. Based on the results of consideration of the problem, it should be concluded that timely referral to a specialist, diagnosis and treatment of ENT diseases are necessary conditions for maintaining and improving the physical health of patients and their quality of life