A New Arithmetically Incomplete First- Order Extension of Gl All Theorems of Which Have Cut Free Proofs

Reference [12] introduced a novel formula to formula translation tool (“formulators”) that enables syntactic metatheoretical investigations of first-order modal logics, bypassing a need to convert them first into Gentzen style logics in order to rely on cut elimination and the subformula property. In fact, the formulator tool, as was already demonstrated in loc. cit., is applicable even to the metatheoretical study of logics such as QGL, where cut elimination is (provably, [2]) unavailable. This paper applies the formulator approach to show the independence of the axiom schema _A ! _8xA of the logics M3 and ML3 of [17, 18, 11, 13]. This leads to the conclusion that the two logics obtained by removing this axiom are incomplete, both with respect to their natural Kripke structures and to arithmetical interpretations. In particular, the so modified ML3 is, similarly to QGL, an arithmetically incomplete first-order extension of GL, but, unlike QGL, all its theorems have cut free proofs. We also establish here, via formulators, a stronger version of the disjunction property for GL and QGL without going through Gentzen versions of these logics (compare with the more complex proofs in [2, 8]).This research was partially supported by NSERC grant No. 8250

On the proof-theory of a first-order extension of GL

We introduce a first order extension of GL, called ML3, and develop its proof theory via a proxy cut-free sequent calculus GLTS. We prove the highly nontrivial result that cut is a derived rule in GLTS, a result that is unavailable in other known first-order extensions of GL. This leads to proofs of weak reflection and the related conservation result for ML3, as well as proofs for Craig’s interpolation theorem for GLTS. Turning to semantics we prove that ML3 is sound with respect to arithmetical interpretations and that it is also sound and complete with respect to converse well-founded and transitive finite Kripke models. This leads us to expect that a Solovay-like proof of arithmetical completeness of ML3 is possible

On the Tightening of the Standard SDP for Vertex Cover with ell1ell_1 Inequalities

We show that the integrality gap of the standard SDP for vc~on instances of $n$ vertices remains $2-o(1)$ even after the addition of emph{all} hypermetric inequalities. Our lower bound requires new insights into the structure of SDP solutions behaving like $ell_1$ metric spaces when one point is removed. We also show that the addition of all $ell_1$ inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we provide the strongest possible separation between hypermetrics and $ell_1$ inequalities with respect to the tightening of the standard SDP for vc

Bilateral Gonadal Cysts and Late Diagnosis of Androgen Insensitivity Syndrome Treated by Laparoscopic Gonadectomy

Background. Complete androgen insensitivity syndrome is a rare syndrome in which the uterus is absent and testes rather than ovaries are present. Patients usually visit a gynecologist due to primary amenorrhea. Case. A forty-eight-year-old woman with lower abdominal pain and anamnesis of uterus agenesis was operated on due to bilateral cystic masses. A 5 × 3 × 1.2 cm left adnexal cyst revealed the presence of a serous cyst with a hypoplastic ductus deferens. A smaller cyst of the right adnexa revealed immature testis tissue with Leydig-cell hyperplasia. After karyotype and hormonal examinations, laparoscopic gonadectomy was performed. Conclusion. Attention should be paid in all cyst-removing operations in cases of uterus agenesis, due to the high incidence of malignancy. Not of less importance is the issue of informing the patient in the most appropriate way

Facilitating a “Last Class Workshop” – A tool for course evaluation and evolution

Recognizing that the last session of class at the end of term is often not very materially productive, we searched for a way to make this last class meaningful and functional. In this presentation, we describe our implementation of and research surrounding a workshop oriented towards obtaining real-time course evaluations, and driving course evolution (Bleicher, 2011). During this session we will describe models of the “Last Class Workshop” for in-person learning as well as both synchronous and asynchronous online learning environments, alongside data speaking to its success in these environments (Styles & Polvi 2022). We will describe the preparative work required of students and instructors. The success of the “Last Class Workshop” depends on the openness of the facilitator to accepting feedback of all types, and on the active engagement and deliberate self-reflection of students (Bovill et al., 2011, Pintrich, 2004), and much of the preparation before the session is oriented towards appropriately framing it for success in these areas. We’ll invite the audience to participate in a mock mini-workshop to illustrate the dynamics and utility of this tool. Fundamentally, the “Last Class Workshop” is built on the idea that the students themselves are the best source of constructive critique, innovative adaptations, and meaningful updates in a course. It is not difficult to implement, has a noticeable impact on participants, and can provide transformative feedback. This research was approved by the University of Toronto Research Ethics Board Protocol #42582 and #40718

An Arithmetically Complete Predicate Modal Logic

This paper investigates a first-order extension of GL called $\textup{ML}^3$. We outline briefly the history that led to $\textup{ML}^3$, its key properties and some of its toolbox: the \emph{conservation theorem}, its cut-free Gentzenisation, the ``formulators'' tool. Its semantic completeness (with respect to finite reverse well-founded Kripke models) is fully stated in the current paper and the proof is retold here. Applying the Solovay technique to those models the present paper establishes its main result, namely, that $\textup{ML}^3$ is arithmetically complete. As expanded below, $\textup{ML}^3$ is a first-order modal logic that along with its built-in ability to simulate general classical first-order provability―"$\Box$" simulating the the informal classical "$\vdash$"―is also arithmetically complete in the Solovay sense

Μελέτη της αυθόρμητης πόλωσης λεπτών υμενίων προπανάλης και εστέρων σε χαμηλές θερμοκρασίες

Σκοπός της παρούσας ερευνητικής εργασίας είναι η μελέτη του φαινομένου της αυθόρμητης πόλωσης που εμφανίζεται κατά την απόθεση ατμών πολικών μορίων σε χαμηλές θερμοκρασίες πάνω σε μεταλλικό υπόστρωμα. Οι ενώσεις που μελετήθηκαν είναι η προπανάλη, ο οξικός μεθυλεστέρας, ο οξικός αιθυλεστέρας, ο οξικός προπυλεστέρας, ο οξικός βουτυλεστέρας και ο οξικός πεντυλεστέρας. Οι αποθέσεις πραγματοποιηθήκαν σε θερμοκρασίες από 33 K έως 135 K πάνω σε πολυκρυσταλλικό φύλλο λευκόχρυσου. Το πείραμα διεξήχθη σε θάλαμο υψηλού κενού εφοδιασμένο με φασματογράφο μάζας τετραπόλου και ηλεκτρόδιο Kelvin. Κάθε κύκλος μετρήσεων περιελάμβανε απόθεση της εκάστοτε ένωσης στο μεταλλικό φύλλο στην επιθυμητή θερμοκρασία, λήψη μέτρησης αρχικής τάσης, σάρωση θερμοκρασίας (προς τη θερμοκρασία δωματίου) με ταυτόχρονη λήψη μετρήσεων τάσης μέχρι την επιστροφή της σε επίπεδα προ αποθέσεως. Διαπιστώθηκε η μη γραμμική εξάρτηση του δυναμικού επιφανείας από την θερμοκρασία απόθεσης, η γραμμική εξάρτηση του δυναμικού από το πλήθος των αποτιθέμενων μορίων και η επίδραση που έχει η θερμοκρασία απόθεσης στο βαθμό πολώσεως της εκάστοτε ένωσης.In this thesis, the phenomenon of spontaneous polarization is studied which occurs when thin films of organic polar molecules are deposited onto a metallic substrate at low temperatures. The compounds examined were propanal, methyl acetate, ethyl acetate, propyl acetate, butyl acetate and amyl acetate. Depositions were carried out at temperatures ranging from 33 K to 135 K onto a polycrystalline platinum foil. The whole experiment was conducted inside a high vacuum chamber equipped with a quadrupole mass spectrometer and a Kelvin probe. Every cycle of measurements consisted of depositing each compound onto the substrate at the desired temperature, taking a starting voltage reading from the Kelvin probe, ramping up the temperature while continuing monitoring the voltage until it dropped to pre-deposition levels. The non-linear dependence of the surface potential on the deposition temperature was confirmed. The surface potential was found to be linearly dependant on the number of deposited molecules. The effect that the deposition temperature has on the degree of polarization was showed

A Short and Readable Proof of Cut Elimination for Two First-Order Modal Logics

A well established technique toward developing the proof theory of a Hilbert-style modal logic is to introduce a Gentzen-style equivalent (a Gentzenisation), then develop the proof theory of the latter, and finally transfer the metatheoretical results to the original logic (e.g., [1, 6, 8, 18, 10, 12]). In the first-order modal case, on one hand we know that the Gentzenisation of the straightforward first-order extension of GL, the logic QGL, admits no cut elimination (if the rule is included as primitive; or, if not included, then the rule is not admissible [1]). On the other hand the (cut-free) Gentzenisations of the first-order modal logics M3 and ML3 of [10, 12] do have cut as an admissible rule. The syntactic cut admissibility proof given in [18] for the Gentzenisation of the propositional provability logic GL is extremely complex, and it was the basis of the proofs of cut admissibility of the Gentzenisations of M3 and ML3, where the presence of quantifiers and quantifier rules added to the complexity and length of the proof. A recent proof of cut admissibility in a cut-free Gentzenisation of GL is given in [5] and is quite short and easy to read. We adapt it here to revisit the proofs for the cases of M3 and ML3, resulting to similarly short and easy to read proofs, only slightly complicated by the presence of quantification and its relevant rules.This research was partially supported by NSERC grant No. 8250

Depurination of Brome mosaic virus RNA3 inhibits its packaging into virus particles

Packaging of the segmented RNA genome of Brome mosaic virus (BMV) into discrete particles is an essential step in the virus life cycle; however, questions remain regarding the mechanism of RNA packaging and the degree to which the viral coat protein controls the process. In this study, we used a plant-derived glycosidase, Pokeweed antiviral protein, to remove 14 specific bases from BMV RNA3 to examine the effect of depurination on virus assembly. Depurination of A771 within ORF3 and A1006 in the intergenic region inhibited coat protein binding and prevented RNA3 incorporation into particles. The disruption of interaction was not based on sequence identity, as mutation of these two purines to pyrimidines did not decrease coat protein-binding affinity. Rather, we suggest that base removal results in decreased thermodynamic stability of local RNA structures required for packaging, and that this instability is detected by coat protein. These results describe a new level of discrimination by coat protein, whereby it recognizes damage to specific viral RNA elements in the form of base removal and selects against incorporating the RNA into particles