The Cosmic Microwave Background Spectrum and a Determination of Fractal Space Dimensionality

The possibility to constrain fractal space dimensionality from Astrophysics and other areas is briefly reviewed. Assuming such dimensionality to be $3 + \epsilon$, a limit to $\epsilon$ can be inferred from COBE satellite data. The available data for the cosmic microwave background radiation spectrum are fitted by a Planck's radiation distribution generalized to non integer space dimensionality. Our analysis shows that the shape of the CMBR spectrum, which does not depend on the absolute normalization, is correctly described from this distribution provided the absolute temperature is equal to 2.726 $\pm$ $0.003\times 10^{-2}$ K and $\epsilon = - (0.957 \pm 0.006) \times 10^{-5}$. This value for $\epsilon$ is shown to be consistent with what is found on a very different spatial scale based on a quantum field phenomenon. The $|\epsilon|$ is interpreted as an upper limit for how much space dimensionality could have deviated from three. In other words, this is the maximum fluctuation space dimensionality should have experienced in a spatial and temporal scale compared to that of the decoupling era.Comment: 6 pages, 2 figure

Gestures as an interface of performers’ intentionality : a case study of Western Embodiment of Karnatic Music in piano performance

Background Music performance has a strong corporeal dimension, involving different types of gestures (technical gestures, expressive gestures, etc.) that performers employ to transform a written score into live music (Leman 2007). This transformation is based on the musical intentions that arise from the performers’ personal interpretation of the composition as an outcome of their artistic praxis, which leads to decisions on how to play the music in terms of its structure, articulation of the phrases, dynamics, timber and the necessary motor strategies to realize these decisions in the sounding music. Aims This research wants to investigate musical gestures as an interface of performers’ intentionality, i.e. an outcome of the artistic praxis and the process of embodiment, in the light of the recent theories on enactment and embodied music cognition (Leman 2016). For this reason, we considered a case study based on the interpretation of a piece that includes the acquisition and embodiment of musical knowledge quite knew to the performer in order to map the modifications in the corporeal engagement from an intuitive approach to a conscious approach. The composition chosen was a contemporary piano piece based on a non-western music tradition: the Karnatic modes from South India. Method To assist the performer in (re)framing the phases of her artistic process, a methodology, called performer based analysis method (Caruso et al 2016), was developed to establish also the procedures of a performative experiment where the performance of the 8th cycle from the 72 Etudes Karnatiques pour piano by Jacques Charpentier (b.1933) was taken as a case study. The performative experiment required a period of preparation, which concerns the performer/researcher’s artistic praxis (to embody the piece) and the self-observation of a video recording archive of her performances in order to map and describe the artistic praxis. The pianist conducted a musicological research on the influence of Indian music in the French contemporary piano repertoire to enrich specifically her current competences in Karnatic Music and had a collaborative three years practice with the composer and with two experts in Karnatic music, a singer and a dancer (see the Re-Orient project: http://re-orient.wixsite.com/indiandream). A retrospective thinking-aloud procedure (Van den Haak & De Jong, 2003) was used during the experiment to allow the performer in rendering explicit and systematic the artistic reflections. The experiment was recorded by a video camera, a microphone and the Motion Capture System. Results To catch the development between the initial intuitive performance and the final embodied performance, two recordings of one fragment from the piece played with these two different approaches (intuitive and conscious) were compared. The analysis of these fragments was based on an alignment between qualitative data acquired through subjective descriptions - based on a performance model and a score annotation - and quantitative data (objective measurements) produced by the audio-video and motion capture recordings. The qualitative and quantitative data (audio and video) were processed through the ELAN software. Gestural similarities and differences between the intuitive and conscious versions were detected by comparing the kinematic and audio measurements (quantitative data) with the performer’s subjective annotations (qualitative data) concerning the motor strategies and the interpretative cues. The results show a different corporeal engagement of the pianist related to the different intentions through a parallel configuration of these two different subjective and objective layers. Conclusions The actual investigation wants to present musical gestures as vehicles of idiosyncratic intentions and expressions by linking performers’ corporeal engagement to the embodiment of their interpretation in order to better understand the connection between musical intentions, goal actions and sound. The role of the technology-mediated approach (thirdperson’s perspective) gives the opportunity to study, as in a mirror-like tool, some aspects, which imply the performer’s subjective involvement (first-person’s perspective). This method provides specifically to musicians/researchers an easier access to music performance analysis. Furthermore, with the implementation of a transdisciplinary and collaborative practice (with the composer, the Indians singer and dancer) plus the aid of technology with the motion and audio analysis, the actual study adds an alternative perspective concerning the exploration and the design of new paths within the field of artistic research

Life and Space Dimensionality: A Brief Review of Old and New Entangled Arguments

A general sketch on how the problem of space dimensionality depends on anthropic arguments is presented. Several examples of how life has been used to constraint space dimensionality (and vice-versa) are reviewed. In particular, the influences of three-dimensionality in the solar system stability and the origin of life on Earth are discussed. New constraints on space dimensionality and on its invariance in very large spatial and temporal scales are also stressed

Experimenting with subjectivity instantiated into gestures “My soul at my fingertips” : My Avatar and Me

Recalling a sentence by the famous French pianist and pedagogue Marie Jaëll-Trautmann who said, “I will play with my soul at my fingertips”, I reflected on the role of performing gestures as an objectifiable aspect of the performer’s subjectivity. Music performance implies a union between soul/mind and body which instantiates the sound message as a felt experience. The energetic tension produced by the “soul” in the creative act of performing is spread at first throughout the entire body to reach finally the “fingertips”. Focusing on the primary role of the body in performance as a potential vehicle to capture subjectivism, I asked myself: What would happen if I visualize my performing body by projecting it into a “body image”, an avatar? Can I use this pragmatic avatar of my-self to look at my subjectivity from an outsider’s perspective? Can I identify my lived experience as instantiated in my gestures through the lens of self-objectification based on empirical data? The assumptions concerning the body as an interface of the performer’s intentionality in terms of sound producing and expressivity inspired me to investigate on my subjectivity through a “performative experiment” combining self-reflections and objective measurements of my bodily expressions during a performance. My performative presentation wants to bring alive the dialectic relation between subjectivity and objectivity in piano performance practice by alternating my live piano performance with interactive reflections on my captured avatar projected on a screen as an objectification of my-self. From this specific angle, my presentation aims at experimenting with subjectivity the creative act of performing instantiated into gestures as a tactile sensation expressing the soul’s intentions. This approach constitutes a connection between gestures and intentionality in music performance and a mediation between scientific understanding and artistic concern

Random matrix over a DVR and LU factorization

Let R be a discrete valuation ring (DVR) and K be its fraction field. If M is a matrix over R admitting a LU decomposition, it could happen that the entries of the factors L and U do not lie in R, but just in K. Having a good control on the valuations of these entries is very important for algorithmic applications. In the paper, we prove that in average these valuations are not too large and explain how one can apply this result to provide an efficient algorithm computing a basis of a coherent sheaf over A^1 from the knowledge of its stalks.Comment: 23 page

A family of pseudo-Anosov braids whose super summit sets grow exponentially

We prove that the size of the super summit set of a braid can grow exponentially with the canonical length of the braid, even for pseudo-Anosov braids

A New Athenian Gymnasium from the 4th Century BC?

Schriftquellen belegen, dass das Gymnasium der Athener Akademie vom 6. Jh. v. Chr. bis mindestens zum 2. Jh. n. Chr. benutzt wurde. Der Ort wurde anhand von Texten und einem Horosstein lokalisiert und seit 1929 mehrfach untersucht. Zu den freigelegten Strukturen gehören im Süden ein recht­eckiger Bau mit Hof, der als Palaestra der Akademie gedeutet wurde, und im Norden ein großer quadratischer Peristylbau, der wenig beachtet wurde. Dieser Beitrag revidiert die Identifizierung der beiden Bauten. Es wird gezeigt, dass der Hof des südlichen Baus in die Spätantike gehört und nicht als Palaestra fungiert haben kann. Stattdessen ist der quadratische Bau, dessen Peristyl von Räumen umgeben und der ins 4. Jh. v. Chr. zu datieren ist, anhand von Plan und Inschriften als Palaestra zu identifizieren

Resultants and subresultants of p-adic polynomials

We address the problem of the stability of the computations of resultants and subresultants of polynomials defined over complete discrete valuation rings (e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms are highly unstable on average and we explain, in many cases, how one can stabilize them without sacrifying the complexity. On the way, we completely determine the distribution of the valuation of the principal subresultants of two random monic p-adic polynomials having the same degree