Generalized periods and mirror symmetry in dimensions n>3

The predictions of the Mirror Symmetry are extended in dimensions n>3 and are proven for projective complete intersections Calabi-Yau varieties. Precisely, we prove that the total collection of rational Gromov-Witten invariants of such variety can be expressed in terms of certain invariants of a new generalization of variation of Hodge structures attached to the dual variety. To formulate the general principles of Mirror Symmetry in arbitrary dimension it is necessary to introduce the ``extended moduli space of complex structures'' M. An analog M\to H*(X,C)[n] of the classical period map is described and is shown to be a local isomorphism. The invariants of the generalized variations of Hodge structures are introduced. It is proven that their generating function satisfies the system of WDVV-equations exactly as in the case of Gromov-Witten invariants. The basic technical tool utilized is the Deformation theory.Comment: 51 pages, LaTe

Frobenius Manifolds and Formality of Lie Algebras of Polyvector Fields

We construct a generalization of the variations of Hodge structures on Calabi-Yau manifolds. It gives a Mirror partner for the theory of genus=0 Gromov-Witten invariantsComment: 12 pages, AMS-TeX; typos and a sign corrected, appendix added. Submitted to IMR

Intrinsic Dimension Estimation for Robust Detection of AI-Generated Texts

Rapidly increasing quality of AI-generated content makes it difficult to distinguish between human and AI-generated texts, which may lead to undesirable consequences for society. Therefore, it becomes increasingly important to study the properties of human texts that are invariant over text domains and various proficiency of human writers, can be easily calculated for any language, and can robustly separate natural and AI-generated texts regardless of the generation model and sampling method. In this work, we propose such an invariant of human texts, namely the intrinsic dimensionality of the manifold underlying the set of embeddings of a given text sample. We show that the average intrinsic dimensionality of fluent texts in natural language is hovering around the value $9$ for several alphabet-based languages and around $7$ for Chinese, while the average intrinsic dimensionality of AI-generated texts for each language is $\approx 1.5$ lower, with a clear statistical separation between human-generated and AI-generated distributions. This property allows us to build a score-based artificial text detector. The proposed detector's accuracy is stable over text domains, generator models, and human writer proficiency levels, outperforming SOTA detectors in model-agnostic and cross-domain scenarios by a significant margin

Topological Data Analysis for Speech Processing

We apply topological data analysis (TDA) to speech classification problems and to the introspection of a pretrained speech model, HuBERT. To this end, we introduce a number of topological and algebraic features derived from Transformer attention maps and embeddings. We show that a simple linear classifier built on top of such features outperforms a fine-tuned classification head. In particular, we achieve an improvement of about $9\%$ accuracy and $5\%$ ERR on four common datasets; on CREMA-D, the proposed feature set reaches a new state of the art performance with accuracy $80.155$. We also show that topological features are able to reveal functional roles of speech Transformer heads; e.g., we find the heads capable to distinguish between pairs of sample sources (natural/synthetic) or voices without any downstream fine-tuning. Our results demonstrate that TDA is a promising new approach for speech analysis, especially for tasks that require structural prediction. Appendices, an introduction to TDA, and other additional materials are available here - https://topohubert.github.io/speech-topology-webpages/Comment: Accepted to INTERSPEECH 2023 conferenc

Artificial Text Boundary Detection with Topological Data Analysis and Sliding Window Techniques

Due to the rapid development of text generation models, people increasingly often encounter texts that may start out as written by a human but then continue as machine-generated results of large language models. Detecting the boundary between human-written and machine-generated parts of such texts is a very challenging problem that has not received much attention in literature. In this work, we consider and compare a number of different approaches for this artificial text boundary detection problem, comparing several predictors over features of different nature. We show that supervised fine-tuning of the RoBERTa model works well for this task in general but fails to generalize in important cross-domain and cross-generator settings, demonstrating a tendency to overfit to spurious properties of the data. Then, we propose novel approaches based on features extracted from a frozen language model's embeddings that are able to outperform both the human accuracy level and previously considered baselines on the Real or Fake Text benchmark. Moreover, we adapt perplexity-based approaches for the boundary detection task and analyze their behaviour. We analyze the robustness of all proposed classifiers in cross-domain and cross-model settings, discovering important properties of the data that can negatively influence the performance of artificial text boundary detection algorithms

Towards high-quality nitrogen-doped diamond single crystals for X-ray optics

In this manuscript, characterization of single-crystalline (111) plates prepared from type-Ib diamonds with a nitro­gen content of 100–150 ppm by means of high-resolution rocking-curve imaging (RCI) is reported. Contrary to common opinion regarding the intrinsically poor diffraction quality of type-I diamonds, RCI showed the presence of nearly defect-free areas of several millimetres squared in the central part of the diamond plates. The observed broadening of the rocking curves is a result of the cutting and polishing processes, causing strains around the edges of the plates and rare defects. An improvement of the preparation technique will thus allow single-crystalline diamond plates to be made for Laue and Bragg monochromators and beam splitters from type-Ib material with areas large enough to be used as optical elements at fourth-generation synchrotron facilities

Synthetic single crystal diamonds for X-ray optics

In the manuscript we report on characterization of single-crystalline (111) plates prepared from type Ib diamonds with nitrogen content of 100-150 ppm and (100) plates prepared from IIa diamond by means of high-resolution rocking curve imaging (RCI). Contrary to a common opinion about intrinsic poor diffraction quality of type Ib diamonds, RCI showed the presence of nearly defect-free areas of several mm2 in the central part of the (111)-oriented diamond plates. In comparison with the (100)-oriented IIa diamond plates prepared by the same HPHT setup the Ib diamonds possess better diffraction quality. The observed broadening of the rocking curves associates with the cutting and polishing processes, causing strains around the edges of the plates and rare defects. An improvement of preparation technique will thus allow to make single-crystalline diamond plates for Laue and Bragg monochromators and beam splitters from type Ib diamond with areas large enough to be used as wavefront-preserving optical elements at 4th generation synchrotron facilities. Contrary to a common opinion about intrinsically poor diffraction quality of type I diamonds, RCI showed the presence of nearly defect-free areas of several mm2 in the central part of the diamond plates. The observed broadening of the rocking curves results from the cutting and polishing processes, causing strains around the edges of the plates and rare defects. An improvement of preparation technique will thus allow to make single-crystalline diamond plates for Laue and Bragg monochromators and beam splitters from type Ib material with areas large enough to be used as optical elements at 4th generation synchrotron facilities

Experimental Justification of Using Aseptisorb-A and Platelet-Rich Plasma in Endoscopic Treatment of Mold Bleeding Stomach Defects

The aim of this study was to investigate the possibility of applying the biologically active draining sorbent Aseptisorb-A in combination with platelet-rich plasma (PRP) to arrest bleeding of mold stomach defects in dogs. Methods and Results: The experimental study was done on 12 outbred dogs (both sexes). Fibrogastroduodenoscopy (FGDS) was performed on all animals under intravenous anesthesia. During FGDS, two ulcerative defects (pilot and control) were made in the antrum of the stomach at 4-5cm distant from each other. Endoscopic hemostasis in pilot ulcers was achieved with the help of pneumatic insufflation of powder-like Aseptisorb-A (0.3mg) on the bleeding defect with further application of platelet-rich autologous plasma from the animal. Endoscopic treatment of control ulcers was not done; such ulcers were used to estimate the time of spontaneous hemostasis. It was determined that in pilot ulcers after described interventions, bleeding arrest occurred in 3.0|2.5|4.0 sec (Ме | upper quartile | lower quartile) (p<0.01). It was noted that in all pilot ulcers, hemostasis was definitive and there was no recurrence of bleeding. In the control ulcers, bleeding arrest occurred in 29.0|27.5|30.5 sec (p≤0.01). In endoscopic gastroscopy, two cases of the reinitiation of haemorrhages in the form of hematin on ulcers were fixed. The reparative process in pilot ulcers treated with Aseptisorb-A and PRP occurred quicker and more efficiently. Complete healing of pilot ulcers occurred in 8.0|8.0|8.5 days (p≤0.01) with formation of a slight sword-cut, which did not destroy the wall of the organ. Complete healing of control ulcers was identified in 15.0|15.0|16.0 days (P<0.01) with formation of a rough scar, which deformed the organ’s wall. Conclusion: Using the biologically active draining sorbent Aseptisorb-A in combination with PRP in endoscopic treatment of mold bleeding in the defects of stomachs accelerates the reparative process, reduces the time of healing in experimental ulcers, improves the quality of healing and does not damage stomach tissue