Cardinal Properties Research Articles

Guessing models and generalized Laver diamond

We analyze the notion of guessing model, a way to assign combinatorial properties to arbitrary regular cardinals. Guessing models can be used, in combination with inaccessibility, to characterize various large cardinal axioms, ranging from supercompactness to rank-to-rank embeddings. The majority of these large cardinal properties can be defined in terms of suitable elementary embeddings j:Vγ→Vλ. One key observation is that such embeddings are uniquely determined by the image structures j[Vγ]≺Vλ. These structures will be the prototypes guessing models. We shall show, using guessing models M, how to prove for the ordinal κM=jM(crit(jM)) (where πM is the transitive collapse of M and jM is its inverse) many of the combinatorial properties that we can prove for the cardinal j(crit(j)) using the structure j[Vγ]≺Vj(γ). κM will always be a regular cardinal, but consistently can be a successor and guessing models M with κM=ℵ2 exist assuming the proper forcing axiom. By means of these models we shall introduce a new structural property of models of PFA: the existence of a “Laver function” f:ℵ2→Hℵ2 sharing the same features of the usual Laver functions f:κ→Hκ provided by a supercompact cardinal κ. Further applications of our analysis will be proofs of the singular cardinal hypothesis and of the failure of the square principle assuming the existence of guessing models. In particular the failure of square shows that the existence of guessing models is a very strong assumption in terms of large cardinal strength.

A Two-in-One Antibody against HER3 and EGFR Has Superior Inhibitory Activity Compared with Monospecific Antibodies

Extensive crosstalk among ErbB/HER receptors suggests that blocking signaling from more than one family member may be essential to effectively treat cancer and limit drug resistance. We generated a conventional IgG molecule MEHD7945A with dual HER3/EGFR specificity by phage display engineering and used structural and mutational studies to understand how a single antigen recognition surface binds two epitopes with high affinity. As a human IgG1, MEHD7945A exhibited dual action by inhibiting EGFR- and HER3-mediated signaling invitro and invivo and the ability to engage immune effector functions. Compared with monospecific anti-HER antibodies, MEHD7945A was more broadly efficacious in multiple tumor models, showing that combined inhibition of EGFR and HER3 with a single antibody is beneficial.

Share the gain, share the pain? Almost transferable utility, changes in production possibilities, and bargaining solutions

We consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions may preclude transferable utility (a property we call “Almost TU”). Holding the disagreement point fixed, we show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash bargaining and the utilitarian solutions are special cases). We apply the result to policy analysis and to incentive compatibility.

On the consistency strength of the proper forcing axiom

In recent work, the second author extended combinatorial principles due to Jech and Magidor that characterize certain large cardinal properties so that they can also hold true for small cardinals. For inaccessible cardinals, these modifications have no effect, and the resulting principles still give the same characterization of large cardinals. We prove that the proper forcing axiom PFA implies these principles hold for ω 2 . Using this, we argue to show that any of the known methods for forcing models of PFA from a large cardinal assumption requires a strongly compact cardinal. If one forces PFA using a proper forcing, then we get the optimal result that a supercompact cardinal is necessary.

Distribution of dystrophin‐ and utrophin‐associated protein complexes (DAPC/UAPC) in human hematopoietic stem/progenitor cells

Hematopoietic stem cells (HSC) are defined by their cardinal properties, such as sustained proliferation, multilineage differentiation, and self-renewal, which give rise to a hierarchy of progenitor populations with more restricted potential lineage, ultimately leading to the production of all types of mature blood cells. HSC are anchored by cell adhesion molecules to their specific microenvironment, thus regulating their cell cycle, while cell migration is essentially required for seeding the HSC of the fetal bone marrow (BM) during development as well as in adult BM homeostasis. The dystrophin-associated protein complex (DAPC) is a large group of membrane-associated proteins linking the cytoskeleton to the extracellular matrix and exhibiting scaffolding, adhesion, and signaling roles in muscle and non-muscle cells including mature blood cells. Because adhesion and migration are mechanisms that influence the fate of the HSC, we explored the presence and the feasible role of DAPC. In this study, we characterized the pattern expression by immunoblot technique and, by confocal microscopy analysis, the cellular distribution of dystrophin and utrophin gene products, and the dystrophin-associated proteins (α-, β-dystroglycan, α-syntrophin, α-dystrobrevin) in relation to actin filaments in freshly isolated CD34+ cells from umbilical cord blood. Immunoprecipitation assays demonstrated the presence of Dp71d/Dp71Δ110m ∼DAPC and Up400/Up140∼DAPC. The subcellular distribution of the two DAPC in actin-based structures suggests their dynamic participation in adhesion and cell migration. In addition, the particular protein pattern expression found in hematopoietic stem/progenitor cells might be indicative of their feasible participation during differentiation.

Ramsey-like cardinals

AbstractOne of the numerous characterizations of a Ramsey cardinal κ involves the existence of certain types of elementary embeddings for transitive sets of size κ satisfying a large fragment of ZFC. We introduce new large cardinal axioms generalizing the Ramsey elementary embeddings characterization and show that they form a natural hierarchy between weakly compact cardinals and measurable cardinals. These new axioms serve to further our knowledge about the elementary embedding properties of smaller large cardinals, in particular those still consistent with V = L.

Converging histories, reconsidered potentialities: The stem cell and cancer

In the last 15 years, stem cell biology has moved to the forefront of contemporary biomedicine. The recent rise to prominence of this distinctive category of cells rests on hopes of harnessing their unique proliferative powers to create novel cell therapies for a range of devastating and presently incurable diseases. This vision, articulated in the new and still emerging therapeutic paradigm of regenerative medicine has, since the mid-1990s, served as an animating force for stem cell research. Often forgotten in current discussions of stem cell innovation is an earlier chapter in stem cell-based therapy, that of bone marrow transplantation (BMT). Used as an adjunct to radio- and/or chemotherapy for cancer, the clinical pedigree of BMT stretches back to the late 1950s. Its therapeutic utility rests on the regenerative powers of the blood stem cell understood to be resident in the bone marrow. Common to BMT and current formulations of stem cells as regenerative therapies is an understanding of stem cells as a biological force for good. However, this may not be the whole story: stem cells may have a ‘dark side’ – one in which they may have a role in the pathogenesis of some forms of cancer. Today, this unsettling possibility finds form in the concept of the cancer stem cell (CSC). This posits a pathological counterpart to the ‘normal’ stem cell: in this model, the leukaemia-causing lesion is resident within an aberrant stem cell – the cancer stem cell – which gives rise to malignant tissue that is a ‘caricature’ of its normal counterpart. Here, in the movement from the normal to the pathological, the cardinal properties of the stem cell become a deadly force: the twin powers of self-renewal and proliferation serving to initiate, drive and sustain tumour growth. Seemingly, the more that is known about stem cells the less certain we are about their capabilities and their potential(s). In an era entranced by the idea of cellular therapies, the shadow cast by the cancer stem cell serves as a signal for caution in the future clinical use of stem cells. Focusing on the leukaemias, this article considers how the histories of BMT and the CSC each contain lessons for the future and emphasizes how our understanding of contemporary science is enriched by an appreciation of its past.

Riffs on the infinite ping-pong ball conundrum

This article presents a novel re-conceptualisation to a well-known problem – The Ping-Pong Ball Conundrum. We introduce a variant of this super-task by considering it through the lens of ‘measuring infinity’ – a conceptualisation of infinity that extrapolates measuring properties of numbers, rather than cardinal properties. This approach is consistent with a nonstandard analysis approach to infinite numbers, and gives credence to the intuitive (but otherwise normatively incorrect) resolution. We explore the mathematical motivation and consequences of this variant, as well as offer further ‘riffs’ on the infinite ball problem for consideration.

Numerical Abstraction via the Frege Quantifier

This paper presents a formalization of rst-order arith- metic characterizing the natural numbers as abstracta of the equinumerosity relation. The formalization turns on the interac- tion of a non-standard (but still rst-order) cardinality quantier with an abstraction operator assigning objects to predicates. The project draws its philosophical motivation from a non-reductionist conception of logicism, a deationary view of abstraction, and an approach to formal arithmetic that emphasizes the cardinal properties of the natural numbers over the structural ones. | binding one (or more) variables and taking two formulas ' and as arguments, assert- ing that there are no more ''s than 's. Using the Frege quantier it is cleraly possible to dene the equinumerosity of ' and , by say- ing that there and no more ''s than 's and vice-versa. The second device is an abstraction operator assigning objects to predicates (or, as Frege would say, \concepts), with the intended interpretation that the object assigned to ' is | or perhaps represents | the number of objects satisfying the formula '. The interaction of these two devices is most notably captured in the so-called \Hume's Principle (HP), the statement that the number of ''s equals the number of 's if and only if the ''s are equinumerous to the 's.

Some consequences of reflection on the approachability ideal

We study the approachability ideal I [ κ + ] \mathcal {I}[\kappa ^+] in the context of large cardinals and properties of the regular cardinals below a singular κ \kappa . As a guiding example consider the approachability ideal I [ ℵ ω + 1 ] \mathcal {I}[\aleph _{\omega +1}] assuming that ℵ ω \aleph _\omega is a strong limit. In this case we obtain that club many points in ℵ ω + 1 \aleph _{\omega +1} of cofinality ℵ n \aleph _n for some n > 1 n>1 are approachable assuming the joint reflection of countable families of stationary subsets of ℵ n \aleph _n . This reflection principle holds under M M \mathsf {MM} for all n > 1 n>1 and for each n > 1 n>1 is equiconsistent with ℵ n \aleph _n being weakly compact in L L . This characterizes the structure of the approachability ideal I [ ℵ ω + 1 ] \mathcal {I}[\aleph _{\omega +1}] in models of M M \mathsf {MM} . We also apply our result to show that the Chang conjecture ( κ + , κ ) ↠ ( ℵ 2 , ℵ 1 ) (\kappa ^+,\kappa )\twoheadrightarrow (\aleph _2,\aleph _1) fails in models of M M \mathsf {MM} for all singular cardinals κ \kappa .

A Simple Cross-Country Index of Trade Specialization

We propose a cross-country specialization index - the B ⋆ - defined as the share of a given product in total country’s exports “normalized” by the average share across all countries. This indicator draws from the Revealed Comparative Advantage index suggested by Balassa (Manch Sch Econ Soc Stud 33(2):99–123, 1965), but its dynamic and cardinal properties are more suitable to perform a cross-country analysis over time. This feature is illustrated with a simple two-country by two-product stylized example and complemented with empirical evidence derived from 79 countries/groups of countries and four distinct technological sectors since the late sixties. We also provide empirical evidence on the external shape of the distribution of the B ⋆ and on its intra-distribution dynamics in different technological sectors. The results indicate that the overall degree of specialization is higher for high-tech exports than for low-tech exports. From a dynamic point of view, there is evidence of significant persistence of the cross-country export patterns.

Share the Gain, Share the Pain? Almost Transferable Utility, Changes in Production Possibilities, and Bargaining Solutions

Consider an n-person economy in which efficiency is independent of distribution but the cardinal properties of the agents’ utility functions precludes transferable utility (a property we call “Almost TU”). We show that Almost TU is a necessary and sufficient condition for all agents to either benefit jointly or suffer jointly with any change in production possibilities under well-behaved generalized utilitarian bargaining solutions (of which the Nash Bargaining and the utilitarian solutions are special cases). We apply the result to household decision-making in the contex of the Rotten Kid Theorem and in evaluating a change in family taxation.

Large cardinals and definable well-orders on the universe

AbstractWe use a reverse Easton forcing iteration to obtain a universe with a definable well-order, while preserving the GCH and proper classes of a variety of very large cardinals. This is achieved by coding using the principle , at a proper class of cardinals κ. By choosing the cardinals at which coding occurs sufficiently sparsely, we are able to lift the embeddings witnessing the large cardinal properties without having to meet any non-trivial master conditions.

VQT: value cardinality and query pattern based R-schema to XML schema translation with implicit referential integrity

In this paper, we propose a new relational schema (R-schema) to XML schema translation algorithm, VQT, which analyzes the value cardinality and user query patterns and extracts the implicit referential integrities by using the cardinality property of foreign key constraints between columns and the equi-join characteristic in user queries. The VQT algorithm can apply the extracted implied referential integrity relation information to the R-schema and create an XML schema as the final result. Therefore, the VQT algorithm prevents the R-schema from being incorrectly converted into the XML schema, and it richly and powerfully represents all the information in the R-schema by creating an XML schema as the translation result on behalf of the XML DTD.

Latent Stem and Progenitor Cells in the Hippocampus Are Activated by Neural Excitation

The regulated production of neurons in the hippocampus throughout life underpins important brain functions such as learning and memory. Surprisingly, however, studies have so far failed to identify a resident hippocampal stem cell capable of providing the renewable source of these neurons. Here, we report that depolarizing levels of KCl produce a threefold increase in the number of neurospheres generated from the adult mouse hippocampus. Most interestingly, however, depolarizing levels of KCl led to the emergence of a small subpopulation of precursors (approximately eight per hippocampus) with the capacity to generate very large neurospheres (> 250 microm in diameter). Many of these contained cells that displayed the cardinal properties of stem cells: multipotentiality and self-renewal. In contrast, the same conditions led to the opposite effect in the other main neurogenic region of the brain, the subventricular zone, in which neurosphere numbers decreased by approximately 40% in response to depolarizing levels of KCl. Most importantly, we also show that the latent hippocampal progenitor population can be activated in vivo in response to prolonged neural activity found in status epilepticus. This work provides the first direct evidence of a latent precursor and stem cell population in the adult hippocampus, which is able to be activated by neural activity. Because the latent population is also demonstrated to reside in the aged animal, defining the precise mechanisms that underlie its activation may provide a means to combat the cognitive deficits associated with a decline in neurogenesis.

Forcing Axioms, Supercompact Cardinals, Singular Cardinal Combinatorics

The purpose of this communication is to present some recent advances on the consequences that forcing axioms and large cardinals have on the combinatorics of singular cardinals. I will introduce a few examples of problems in singular cardinal combinatorics which can be fruitfully attacked using ideas and techniques coming from the theory of forcing axioms and then translate the results so obtained in suitable large cardinals properties.The first example I will treat is the proof that the proper forcing axiom PFA implies the singular cardinal hypothesis SCH, this will easily lead to a new proof of Solovay's theorem that SCH holds above a strongly compact cardinal. I will also outline how some of the ideas involved in these proofs can be used as means to evaluate the “saturation” properties of models of strong forcing axioms like MM or PFA.The second example aims to show that the transfer principle (ℵω+1, ℵω) ↠ (ℵ2, ℵ1) fails assuming Martin's Maximum MM. Also in this case the result can be translated in a large cardinal property, however this requires a familiarity with a rather large fragment of Shelah's pcf-theory.Only sketchy arguments will be given, the reader is referred to the forthcoming [25] and [38] for a thorough analysis of these problems and for detailed proofs.

Comparative effects of the α7 nicotinic partial agonist, S 24795, and the cholinesterase inhibitor, donepezil, against aging-related deficits in declarative and working memory in mice

The comparative effects of a newly described specific alpha7 nAChR partial agonist, S 24795, and a cholinesterase inhibitor, donepezil, currently used as a symptomatic Alzheimer's disease treatment were studied in two mouse models of aging-related memory deficits. We employed radial arm-maze paradigms assessing short-term working memory (STWM, experiment A) and mnemonic flexibility, a cardinal property of long-term declarative (LTDM, experiment B). Both compounds were administered daily at 0.3 and 1 mg/kg subcutaneously (~3 weeks). In the STWM experiment, vehicle-treated aged mice displayed a severe and persistent deficit in the retention of successive arm visits in comparison to younger controls. S 24795 at 1 mg/kg (trends at 0.3 mg/kg) and donepezil at 0.3 mg/kg (but not 1 mg/kg) exerted beneficial effects on this deficit: The performance of aged mice treated with these drugs remarkably increased across the testing days and almost reached young adult performance level. In the critical test trials of memory flexibility (i.e., LTDM), in experiment B, S 24795 at 1 mg/kg (trends at 0.3 mg/kg) and donepezil at the dose of 1 mg/kg (but not 0.3 mg/kg) improved aged mice performance. This preclinical demonstration that S 24795 restored specific age-related memory deficits with as much efficacy as donepezil adds to recent literature in highlighting the potential interest of an alpha7 nAChR drug as a symptomatic AD therapeutic.

A note on small income effects

This note provides an alternative sufficient condition for the small income effect result that is first shown by Vives [Small income effects: a Marshallian theory of consumer surplus and downward sloping demand, Rev. Econ. Stud. 54(1) (1987) 87–103]. The condition is stated by ordinal terms only, whereas Vives assumes cardinal properties of utility representation. Second, as its application, we provide a sufficient condition for the preference being asymptotically quasi-linear, in a two good economy where the second good is a composition of a large number of goods.

Double helix in large large cardinals and iteration of elementary embeddings

We consider iterations of general elementary embeddings and, using this notion, point out helices of consistency-wise implications between large large cardinals. Up to now, large cardinal properties have been considered as properties which cannot be accessed by any weaker properties and it has been known that, with respect to this relation, they form a proper hierarchy. The helices we point out significantly change this situation: the same sequence of large cardinal properties occurs repeatedly, changing only the parameters. As results of our investigation of this helical structure, we have (i) new characterizations of extendible cardinals and of Vopěnkan cardinals in terms of elementary embeddings from the universe V , (ii) a new large large cardinal property which looks like Shelahness properly between Vopěnkaness and almost hugeness, and (iii) a more direct relation between Vopěnkaness and Woodinness than already known. We also consider limits of the helices and relations with the axioms I1–I3.

Odor representation in the anterior piriform cortex of an in vitro isolated whole brain with the olfactory epithelium

isual detection of motion is one of cardinal property of human brain. In his study, we investigated how spatial extent of motion stimulus affects uman brain response using 306 ch whole head magnetoencephalograph MEG). We recorded MEG response to motion onset of sinusoidal gratng with different size (2.2× 2.9◦ to 44.8× 57.4◦) and speed (2.9◦/s to 3.5◦/s). The first component of MEG response (peaked at 114–216ms) as observed around occipito-temporal area. The latency and amplitude as affected by the motion speed as previous study for the second and hird stimulus sizes. The latency was also affected by the stimulus size nd was the shortest at the second largest stimulus size. In contrast, the mplitude was not affected by the size. The results show that the motion ize affects human brain response in a manner different from motion peed, suggesting that the neural process of motion detection interacts ith neural information about spatial extent of motion image.