On the Union Closed Fragment of Existential Second-Order Logic and Logics with Team Semantics

We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables the handling and provides a better understanding of this fragment. We also introduce inclusion-exclusion games that turn out to be precisely the corresponding model-checking games. These games are not only interesting in their own right, but they also are a key factor towards building a bridge between the semantic and syntactic fragments. On the level of logics with team semantics we additionally present restrictions of inclusion-exclusion logic to capture the union closed fragment. Moreover, we define a team based atom that when adding it to first-order logic also precisely captures the union closed fragment of existential second-order logic which answers an open question by Galliani and Hella

Fragments of existential second-order logic and logics with team semantics

In this thesis different fragments of logics with team semantics and of existential second-order logic will be studied. The fragments we are interested in are the union closed fragments of these logics, inclusion logic of restricted arity and variants of logics with team semantics using dependency concepts which can distinguish elements only up to a given equivalence. Logics with team semantics are extensions of first-order logic that allow to express concepts like (in)dependence in the form of atomic statements. To this end formulae are not evaluated against a single assignment but against so-called teams which are sets of such assignments. There is a strong connection between these logics and ESO, the existential fragment of second-order logic, which is reflected in the possibility to express formulae of logics with team semantics as equivalent ESO-sentences with an additional predicate for the team and vice versa. Dependence logic goes back to Väänänen and has the same expressive power as the fragment of ESO in which the team predicate occurs only negatively. Independence logic, introduced by Grädel und Väänänen, has, as Galliani has proved, the full expressive power of ESO and is equivalent to inclusion-exclusion logic, in whose formulae so-called in- resp.~exclusion atoms can be used. If one allows only in- or only exclusion atoms, one speaks of the in- or exclusion logic. The latter corresponds exactly to dependence logic, while Galliani and Hella have shown that the inclusion logic corresponds to the greatest fixed-point logic GFP. Even though formulae of inclusion logic are closed under unions, not every union closed formulae is expressible in inclusion logic. This leads to the question how such formulae can be characterised. In this thesis, it will be proved that union closed ESO-sentences can be characterised syntactically by myopic ESO-sentences. Towards this end, we will define and study novel inclusion-exclusion games that are precisely the model-checking games of ESO. Using these games it is also possible to identify a corresponding syntactical fragment of inclusion-exclusion logic. Furthermore, these games give rise to the definition of an atom that, when added to first-order logic, also precisely captures the union-closed fragment. Another, so far open, problem that this thesis deals with is the question of Rönnholm, which fragment of GFP corresponds to the inclusion logic of restricted arity. In this thesis such a fragment is going to be introduced and effective translations between it and the restricted inclusion logic and vice versa are provided. Finally, we study variants of logics with dependency concepts, which can distinguish elements only up to a given equivalence. We juxtapose these new logics with equivalent fragments of ESO and study their expressive powers on different classes of structures

Crystal Structures of α- And β-Nitrogen Trifluoride

The crystal structures of α-NF 3 and β-NF 3 are reported for the first time. As shown by powder neutron diffraction, the lowerature α-NF 3 crystallizes in the orthorhombic space group Pnma (oP16) with lattice parameters a = 6.71457(13) Å, b = 7.30913(14) Å, c = 4.55189(8) Å, V = 223.396(7) Å 3 , and Z = 4 at T = 6 K. The intramolecular atom distances in α-NF 3 are 1.3639(16) and 1.3677(11) Å for N-F, and 2.1216(16) and 2.120(2) Å for F···F. The F-N-F bond angles are 101.92(7)° and 101.63(10)°. All data are in excellent agreement with quantum-chemical predictions and previously reported experimentally obtained gas-phase data. The higherature β-NF 3 is a plastic crystal, space group P4 2 /mnm (tP120), with the lattice parameters a = 15.334(6) Å, c = 7.820(3) Å, V = 1838.6(12) Å 3 , and Z = 30 at T = 60 K. Its crystal structure is closely related to that of the Frank-Kasper sigma phase.Peer reviewe

The Crystal Structures of α- and β-F 2 Revisited

The crystal structures of α-F 2 and β-F 2 have been reinvestigated using neutron powder diffraction. For the low-temperature phase α-F 2 , which is stable below circa 45.6 K, the monoclinic space group C2/c with lattice parameters a=5.4780(12), b=3.2701(7), c=7.2651(17) Å, β=102.088(18)°, V=127.26(5) Å 3 , mS8, Z=4 at 10 K can now be confirmed. The structure model was significantly improved, allowed for the anisotropic refinement of the F atom, and an F−F bond length of 1.404(12) Å was obtained, which is in excellent agreement with spectroscopic data and high-level quantum chemical predictions. The high-temperature phase β-F 2 , stable between circa 45.6 K and the melting point of 53.53 K, crystallizes in the cubic primitive space group Pm (Formula presented.) n with the lattice parameter a=6.5314(15) Å, V=278.62(11) Å 3 , cP16, Z=8, at 48 K. β-F 2 is isotypic to γ-O 2 and δ-N 2 . The centres of gravity of the F 2 molecules are arranged like the atoms in the Cr 3 Si structure type.Peer reviewe

Amplification of N-Myc is associated with a T-cell-poor microenvironment in metastatic neuroblastoma restraining interferon pathway activity and chemokine expression

Immune checkpoint inhibitors have significantly improved the treatment of several cancers. T-cell infiltration and the number of neoantigens caused by tumor-specific mutations are correlated to favorable responses in cancers with a high mutation load. Accordingly, checkpoint immunotherapy is thought to be less effective in tumors with low mutation frequencies such as neuroblastoma, a neuroendocrine tumor of early childhood with poor outcome of the high-risk disease group. However, spontaneous regressions and paraneoplastic syndromes seen in neuroblastoma patients suggest substantial immunogenicity. Using an integrative transcriptomic approach, we investigated the molecular characteristics of T-cell infiltration in primary neuroblastomas as an indicator of pre-existing immune responses and potential responsiveness to checkpoint inhibition. Here, we report that a T-cell-poor microenvironment in primary metastatic neuroblastomas is associated with genomic amplification of the MYCN (N-Myc) proto-oncogene. These tumors exhibited lower interferon pathway activity and chemokine expression in line with reduced immune cell infiltration. Importantly, we identified a global role for N-Myc in the suppression of interferon and pro-inflammatory pathways in human and murine neuroblastoma cell lines. N-Myc depletion potently enhanced targeted interferon pathway activation by a small molecule agonist of the cGAS-STING innate immune pathway. This promoted chemokine expression including Cxcl10 and T-cell recruitment in microfluidics migration assays. Hence, our data suggest N-Myc inhibition plus targeted IFN activation as adjuvant strategy to enforce cytotoxic T-cell recruitment in MYCN-amplified neuroblastomas

Adoptive T Cell Therapy Targeting Different Gene Products Reveals Diverse and Context-Dependent Immune Evasion in Melanoma

Tumor immune escape limits durable responses to T cell therapy. Here, we examined how regulation and function of gene products that provide the target epitopes for CD8(+) T cell anti-tumor immunity influence therapeutic efficacy and resistance. We used a CRISPR-Cas9-based method (CRISPitope) in syngeneic melanoma models to fuse the same model CD8(+) T cell epitope to the C-termini of different endogenous gene products. Targeting melanosomal proteins or oncogenic CDK4(R24C )(Cyclin-dependent kinase 4) by adoptive cell transfer (ACT) of the same epitope-specific CD8(+) T cells revealed diverse genetic and non-genetic immune escape mechanisms. ACT directed against melanosomal proteins, but not CDK4(R24C), promoted melanoma dedifferentiation, and increased myeloid cell infiltration. CDK4(R24C) antigen persistence was associated with an interferon-high and T-cell-rich tumor microenvironment, allowing for immune checkpoint inhibition as salvage therapy. Thus, the choice of target antigen determines the phenotype and immune contexture of recurrent melanomas, with implications to the design of cancer immunotherapies