Knowledge from Non-Knowledge in Wittgenstein's _On Certainty_: A Dialogue

Remarks in Wittgenstein’s On Certainty present a view according to which all knowledge rests on commitments to things we do not know. In his usual manner, Wittgenstein does not present a clearly defined set of premises designed to support this view. Instead, the reasons emerge along with the view through a series of often cryptic remarks. But this does not prevent us from critically assessing the position (or positions) one finds in the work. This paper attempts to do that in the form of a philosophical dialogue. The challenges to Wittgenstein’s view raised here center on: the extent to which hinge commitments can plausibly be regarded as rules of a language-game rather than rationally assessable propositions, mutual support versus bottom up notions of justification, the subject and context relativity of hinge commitments, the difference between justification and persuasion, whether propositions of the form p is hinge are themselves hinge, and the general viability of Wittgenstein’s view as an alternative to epistemological skepticism and Moorean anti-skepticism

Inducing Metallicity in Graphene Nanoribbons via Zero-Mode Superlattices

The design and fabrication of robust metallic states in graphene nanoribbons (GNRs) is a significant challenge since lateral quantum confinement and many-electron interactions tend to induce electronic band gaps when graphene is patterned at nanometer length scales. Recent developments in bottom-up synthesis have enabled the design and characterization of atomically-precise GNRs, but strategies for realizing GNR metallicity have been elusive. Here we demonstrate a general technique for inducing metallicity in GNRs by inserting a symmetric superlattice of zero-energy modes into otherwise semiconducting GNRs. We verify the resulting metallicity using scanning tunneling spectroscopy as well as first-principles density-functional theory and tight binding calculations. Our results reveal that the metallic bandwidth in GNRs can be tuned over a wide range by controlling the overlap of zero-mode wavefunctions through intentional sublattice symmetry-breaking.Comment: The first three authors listed contributed equall

Topological Band Engineering of Graphene Nanoribbons

Topological insulators (TIs) are an emerging class of materials that host highly robust in-gap surface/interface states while maintaining an insulating bulk. While most notable scientific advancements in this field have been focused on TIs and related topological crystalline insulators in 2D and 3D, more recent theoretical work has predicted the existence of 1D symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally-confined, semiconducting strips of graphene is determined by their width, edge shape, and the terminating unit cell, and is characterized by a Z2 invariant (similar to 1D solitonic systems). Interfaces between topologically distinct GNRs characterized by different Z2 are predicted to support half-filled in-gap localized electronic states which can, in principle, be utilized as a tool for material engineering. Here we present the rational design and experimental realization of a topologically-engineered GNR superlattice that hosts a 1D array of such states, thus generating otherwise inaccessible electronic structure. This strategy also enables new end states to be engineered directly into the termini of the 1D GNR superlattice. Atomically-precise topological GNR superlattices were synthesized from molecular precursors on a Au(111) surface under ultra-high vacuum (UHV) conditions and characterized by low temperature scanning tunneling microscopy (STM) and spectroscopy (STS). Our experimental results and first-principles calculations reveal that the frontier band structure of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This novel manifestation of 1D topological phases presents an entirely new route to band engineering in 1D materials based on precise control of their electronic topology, and is a promising platform for future studies of 1D quantum spin physics.Comment: Contains main manuscript and supplemental informatio

Evaluation of DNA Methylation Episignatures for Diagnosis and Phenotype Correlations in 42 Mendelian Neurodevelopmental Disorders.

Genetic syndromes frequently present with overlapping clinical features and inconclusive or ambiguous genetic findings which can confound accurate diagnosis and clinical management. An expanding number of genetic syndromes have been shown to have unique genomic DNA methylation patterns (called episignatures ). Peripheral blood episignatures can be used for diagnostic testing as well as for the interpretation of ambiguous genetic test results. We present here an approach to episignature mapping in 42 genetic syndromes, which has allowed the identification of 34 robust disease-specific episignatures. We examine emerging patterns of overlap, as well as similarities and hierarchical relationships across these episignatures, to highlight their key features as they are related to genetic heterogeneity, dosage effect, unaffected carrier status, and incomplete penetrance. We demonstrate the necessity of multiclass modeling for accurate genetic variant classification and show how disease classification using a single episignature at a time can sometimes lead to classification errors in closely related episignatures. We demonstrate the utility of this tool in resolving ambiguous clinical cases and identification of previously undiagnosed cases through mass screening of a large cohort of subjects with developmental delays and congenital anomalies. This study more than doubles the number of published syndromes with DNA methylation episignatures and, most significantly, opens new avenues for accurate diagnosis and clinical assessment in individuals affected by these disorders